Motor vehicle operators speed, roll through stop signs, don't signal turns or lane changes, and generally break many laws, just like bicycle riders. Any accusation that bicycle riders are worse is open to debate. Half the population is below average, and both drivers and bicyclists have their share of below-average folks.
Looking at the question of speeding/non-speeding: a bicyclist is traffic. As long as the bicycle rider was moving at an appropriate speed for a bicycle rider of his or her age, the bicyclist would have every right to the road that any other road user has.
Normal local roads do not have restrictions on riding bicycles, unlike Interstates in Virginia. Lawmakers on the contrary seem to think that it is a good thing to get the citizenry out riding bicycles for health benefits, air quality benefits, energy conservation benefits, as well as the general dislike of infringing on an individual's freedom to travel, whether on foot, on bicycle, or in a car. In a directly parallel Ohio Supreme Court case which resulted in over a million dollar settlement, the judge upheld the lawful right of the bicycle rider to ride his bicycle on a public road and held that an officer acted illegally when he detained a bicycle rider for essentially the officer's idea of "obstruction of traffic." The judge wrote, ". . . the officer’s testimony is that he felt that the defendant was impeding traffic and that is why he asked him to pull over. It is clear to the court that a bicyclist traveling at a reasonable speed for a bicycle cannot be convicted under R.C. 4511.22. There is no evidence that the defendant here was traveling at anything other than a reasonable speed."
http://www.supremecourt.ohio.gov/rod/docs/pdf/98/2008/2008-Ohio-7142.pdf
Turning to Virginia law, the only remotely related code on obstruction of traffic would probably be the following, if the bicycle were a MOTOR vehicle. Virginia Code
§46.2-877 states that 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.
If one were to wax philosophical, some may argue that freedom to travel is a cherished part of our American political tradition. Any plan to limit access to the roads clashes with a fundamental "Freedom of Movement" for U.S. citizens, which was described in the 1920 Supreme Court case,
UNITED STATES v. WHEELER:
"In all the States from the beginning down to the adoption of the Articles of Confederation the citizens thereof possessed the fundamental right, inherent in citizens of all free governments, peacefully to dwell within the limits of their respective States, to move at will from place to place therein, and to have free ingress thereto and egress therefrom, with a consequent authority in the States to forbid and punish violations of this fundamental right."