Actually, we should have said: riders of bicycles are not bound by rules that apply only to drivers of motor vehicles…
It’s helpful to note that the “rules of the road” apply not to vehicles, or bikes, but rather to the people operating these things. A typical example is the rule for what to do at a stop sign, §28-855(B). “A driver of a vehicle approaching a stop sign shall stop…”. 
In Arizona, bicycles are, by definition, not vehicles; nor are they motor vehicles. Here are those definitions §28-101:
§28-101. Definitions ... 58. "Vehicle" means a device in, on or by which a person or property is or may be transported or drawn on a public highway, excluding devices moved by human power or used exclusively on stationary rails or tracks. 33. "Motor vehicle": (a) Means either: (i) A self-propelled vehicle. (ii) For the purposes of the laws relating to the imposition of a tax on motor vehicle fuel, a vehicle that is operated on the highways of this state and that is propelled by the use of motor vehicle fuel. (b) Does not include a motorized wheelchair, an electric personal assistive mobility device or a motorized skateboard...
This is a cyclist’s fundamental right to the road; the equal of driver’s.
Note well that it refers specifically to the rights and duties of the driver of vehicle — and NOT the driver of MOTOR vehicle, in fact the word motor does not appear at all in 28-812.
It might surprise you to note that the phrase “motor vehicle” occurs only a handful of places in ARS Title 28, Transportation, with respect to how a driver must operate a vehicle. By far, most driver’s duties refer, as in the stop sign example above, simply to vehicle.
Some references are incidental; lane and speed restrictions on motor vehicles weighing over 26,000 pounds (§28-736, §28-709). Another was intended to set minimum passing clearance when a motor vehicle overtakes a bicycle (§28-735). Two germane examples for cyclists are following distance, and impeding traffic.
§28-730, “The driver of a motor vehicle shall not follow another vehicle more closely than is reasonable and prudent…”, without the word motor in this statute, pacelining would likely be illegal. Since reasonable people would probably agree that a couple of inches is an inappropriately small following distance.
§28-704(A), “A person shall not drive a motor vehicle at such a slow speed as to impede or block the normal and reasonable movement of traffic…”. This is what I refer to as the cyclist’s second most fundamental right to the road, because if this statute were to apply to cyclists, then they would in effect be not allowed to use any road where traffic even might be impeded; regardless of number of lanes, width, presence or absence of a bike lane, or anything else. There is some detailed minutia  revolving around what is meant by the “normal and reasonable movement” but that is immaterial to cyclists, since this section is inapplicable to them.
Likewise, §28-701(E) “A person shall not drive a MOTOR vehicle at a speed that is less than the speed that is reasonable and prudent under existing conditions”, never applies to bicyclists.
The point is that the phrase motor vehicle is used sparingly and deliberately to apply only to drivers of that type of vehicle, reflecting clear legislative intent. In the case of 28-704(A) to allow cyclists to use all roads even though motorists might sometimes be impeded (with some caveats: There is a specific allowance for prohibiting bicycles on controlled access highways, and other roads on a case-by-case basis).
 There are actually several variations besides “driver of a vehicle” see the-driver-of-a-vehicle for a fuller taxonomy.
 A small number of states, but not AZ, (see chart below) have an impeding statute that omits the word “motor” making it necessary to show that a cyclist’s use of a roadway is a “normal and reasonable” movement of traffic in order to not be liable for impeding. This was done successfully, e.g in the Trotwood v. Selz case, in a published ruling.
Note that persons riding animals or driving animal drawn vehicles are also drivers of vehicles. See 28-625
That motor vehicle statutes don’t apply to bicyclists needed to be litigated for a number of cases where Flagstaff PD cited a cyclist for 28-701E. The City of Flagstaff’s assistant city prosecutor, Mr. Brown as detailed in this trial transcript; the prosecutor at closing said “MR. BROWN: For Count B, 28-701E, (indiscernible) read the statute, State would have to agree that that statute seems to apply strictly to motor vehicles, since it’s not a moped or anything like that, it’s strictly a bicycle, the statue would not be applicable…”
Other US States
According to iamtraffic :
In 42 US states the law against “impeding traffic” only applies to motor vehicle drivers who impede (not merely delay) other drivers by driving too slowly, typically on freeways. Sadly, 6 US states do NOT exclude bicyclists from the provisions of this law and police sometimes use it as a way to harass cyclists who operate as drivers.
The caselaw from Ohio (where, as noted above in the iamtraffic graphic), where bicyclists are not exempted from the general impeding law, is illuminating. In the published opinion of State v. Selz , 139 Ohio App.3d 947 the appeals court found an operator, in this case a bicyclist, cannot be in violation of the impeding statute as long as the operator’s speed is reasonable for the type of device in use. “We conclude that a bicyclist is not in violation of the ordinance when he is traveling as fast as he reasonably can”. The reasoning is based on a Georgia Appeals court opinion Lott v. Smith (1980), 156 Ga. App. 826 275 S.E.2d 720. that a corn combine (a motor vehicle, by the way) cannot be held in violation of the impeding rule for traveling 17mph on a road with a much higher speed limit and despite the fact that other traffic was clearly being impeded becasue the combine was traveling as fast as is reasonable for a corn combine. Below is the synopsis of the Selz opinion, with
In either [meaning, the Selz/bicycle case, or the Georgia corn combine] case, holding the operator to have violated the slow speed statute would be tantamount to excluding operators of these vehicles from the public roadways, something that each legislative authority, respectively, has not clearly expressed an intention to do.
All this means that Arizona law, even if mis-applied to bicyclists (who are not motorized vehicle. Or for that matter, say, a slow-moving truck driver) could not be held in violation because the legislature has not banned bicyclists (or slow moving trucks) from public roads. Due to the persuasive precedents set by Selz and Lott.
See also the tasering case of Tony Patrick.
The UVC equivalence to ARS:
|§11-1202—Traffic laws apply to persons on bicycles and other human powered vehiclesEvery person propelling a vehicle by human power or riding a bicycle shall have all of the rights and all of the duties applicable to the driver of any other vehicle under chapters 10 and 11, except as to special regulations in this article and except as to those provisions which by their nature can have no application.||§28-812. Applicability of traffic laws to bicycle ridersA person riding a bicycle on a roadway or on a shoulder adjoining a roadway is granted all of the rights and is subject to all of the duties applicable to the driver of a vehicle by this chapter and chapters 4 and 5 of this title, except special rules in this article and except provisions of this chapter and chapters 4 and 5 of this title that by their nature can have no application.|
|§11-805 – Minimum speed regulation(a) No person shall drive a motor vehicle at such a slow speed as to impede the normal and reasonable movement of traffic except when reduced speed is necessary for safe operation or in compliance with law.||28-704. Minimum speed limits; A. A person shall not drive a motor vehicle at such a slow speed as to impede or block the normal and reasonable movement of traffic except when either of the following applies…|
|? can’t find, perhaps the UVC has no slower than R&P?||28-701. Reasonable and prudent speed;E. A person shall not drive a motor vehicle at a speed that is less than the speed that is reasonable and prudent under existing conditions unless the speed that is reasonable and prudent exceeds the maximum safe operating speed of the lawfully operated implement of husbandry.|
Principles of statutory construction and interpretation
This is a pretty good roundup of the principles, as they appear in U.S. Parking Sys v. City of Phoenix, 160 Ariz. 210, 211, 772 P.2d 33, 34 (App. 1989)
We begin our examination … by noting certain principles of statutory construction and interpretation…
Where a term is used in one provision of a statute and omitted from another, that term should not be read into the section where it is omitted. Dunlop v. First Nat’l Bank of Arizona, 399 F. Supp. 855 (D.C.Az. 1975).
28-704A (for example) uses the term ‘motor’ while 28-812 does not. The term ‘motor’ should not be read into 28-704.
An unambiguous statute should be interpreted to mean what it plainly states unless an absurdity results. Holding v. Industrial Comm’n of Arizona, 139 Ariz. 548, 679 P.2d 571 (App. 1984).
28-704A unambiguously applies specifically to drivers of motor vehicles.
While it is true that title headings in statutes are not part of the law… , we can nevertheless refer to titles and captions for indications of legislative intent. State v. Superior Court, 128 Ariz. 535, 627 P.2d 686 (1981).
When a statute sets forth the things on which it will operate, it will be construed to exclude from its effect those not expressly mentioned. Roller Village, Inc. v. Superior Court, 154 Ariz. 195, 741 P.2d 328 (App. 1987).
28-704A operates on drivers of motor vehicle. All others are excluded.
Unless otherwise defined, words in a statute will be interpreted as taking their ordinary common meaning. Fagner, supra; Harrelson v. Industrial Comm’n of Arizona, 144 Ariz. 369, 697 P.2d 1119 (App. 1984)