According to the Texas Transportation code Sec. 551.101. RIGHTS AND DUTIES:
(a) A person operating a bicycle has the rights and duties applicable to a driver operating a vehicle (...)
This means that cyclists and motorists share the same rules (and rights) of the road, which also means that cyclists can receive traffic citations while operating a bicycle on a public roadway*.
Thanks to the work of Austin Cycling Association and other local advocacy groups, cyclists who receive traffic citations on Austin’s roadways can now receive deferral for dismissal of certain bicycle citations, if referred by the court, by taking a Defensive Cycling course. Defensive Driving courses do not present their material as it would pertain to a cyclist’s experience on the road; Austin Cycling Association’s Defensive Cycling course better equips cyclists with the tools and tactics they will need to protect themselves on the road. For more information, visit Austincycling.org.
* Have questions about riding on the sidewalk? In Austin, a person may ride a bicycle on a sidewalk, except where restricted by § 12-2-13 of Austin City Ordinance: Bicycle Traffic Regulations (mostly Central Business District areas)