First, the code on their website should be current.
Found this:
§ 46.2-800. Riding bicycles, electric personal assistive mobility devices, electric power-assisted bicycles, or mopeds; riding or driving animals.
Every person riding a bicycle, electric personal assistive mobility device, electric power-assisted bicycle, moped, or an animal or driving an animal on a highway
shall be subject to the provisions of this chapter and shall have all of the rights and duties applicable to the driver of a vehicle, unless the context of the provision clearly indicates otherwise.
The provisions of subsections A and C of §
46.2-920 applicable to operation of emergency vehicles under emergency conditions shall also apply, mutatis mutandis, to bicycles, electric personal assistive mobility devices, electric power-assisted bicycles, and mopeds operated under similar emergency conditions by law-enforcement officers.
Code 1950, § 46-183; 1958, c. 541, § 46.1-171; 1980, c. 456; 1981, c. 585; 1989, c. 727; 1994, c.
176; 2001, c.
834; 2002, c.
254.
Highlighted in red the relevant part according to your question.
I think this is it:
§ 46.2-905. Riding bicycles, electric personal assistive mobility devices, electric power-assisted bicycles, and mopeds on roadways and bicycle paths.
Any person operating a bicycle, electric personal assistive mobility device, electric power-assisted bicycle, or moped on a roadway at less than the normal speed of traffic at the time and place under conditions then existing shall ride as close as safely practicable to the right curb or edge of the roadway, except under any of the following circumstances:
1. When overtaking and passing another vehicle proceeding in the same direction;
2. When preparing for a left turn at an intersection or into a private road or driveway;
3. When reasonably necessary to avoid conditions including, but not limited to, fixed or moving objects, parked or moving vehicles, pedestrians, animals, surface hazards, or substandard width lanes that make it unsafe to continue along the right curb or edge;
4. When avoiding riding in a lane that must turn or diverge to the right; and
5. When riding upon a one-way road or highway, a person may also ride as near the left-hand curb or edge of such roadway as safely practicable.
For purposes of this section, a "substandard width lane" is a lane too narrow for a bicycle, electric personal assistive mobility device, electric power-assisted bicycle, motorized skateboard or foot-scooter, or moped and another vehicle to pass safely side by side within the lane.
Persons riding bicycles, electric personal assistive mobility devices, or electric power-assisted bicycles on a highway shall not ride more than two abreast. Persons riding two abreast shall not impede the normal and reasonable movement of traffic, shall move into a single file formation as quickly as is practicable when being overtaken from the rear by a faster moving vehicle, and, on a laned roadway, shall ride in a single lane.
Notwithstanding any other provision of law to the contrary, the Department of Conservation and Recreation shall permit the operation of electric personal assistive mobility devices on any bicycle path or trail designated by the Department for such use.
1974, c. 347, § 46.1-229.1; 1980, c. 130; 1981, c. 585; 1989, c. 727; 2001, c.
834; 2002, c.
254; 2003, cc.
29,
46; 2004, cc.
947,
973; 2006, cc.
529,
538; 2007, cc.
209,
366; 2013, c.
783.
I think they just want you to ride as close to the right side of the road. I would call your local DMV and ask them what they think about it. Of course that wouldn't be legal advice but maybe they could offer something. That's what I did. Couldn't afford an attorney. I think as long as you are not impeding traffic and riding out of control you should be fine.
/ I'm not a lawyer nor is this legal advice.