For reference:
Transportation Code 551.101. RIGHTS AND DUTIES. (a) A person operating a bicycle has the rights and duties applicable to a driver operating a vehicle under this subtitle, unless:
(1) a provision of this chapter alters a right or duty; or
(2) a right or duty applicable to a driver operating a vehicle cannot by its nature apply to a person operating a bicycle.
(b) A parent of a child or a guardian of a ward may not knowingly permit the child or ward to violate this subtitle.

Transportation Code Sec. 551.106. REGULATION OF ELECTRIC BICYCLES. (a) The department or a local authority may not prohibit the use of an electric bicycle on a highway that is used primarily by motor vehicles. The department or a local authority may prohibit the use of an electric bicycle on a highway used primarily by pedestrians.
(b) The department shall establish rules for the administration of this section.

Transportation Code 541.201(24)(24) "Electric bicycle" means a bicycle that:
(A) is designed to be propelled by an electric motor, exclusively or in combination with the application of human power;
(B) cannot attain a speed of more than 20 miles per hour without the application of human power; and
(C) does not exceed a weight of 100 pounds.

Local Government Code 217.003(c) The governing body may restrain or prohibit the firing of firecrackers or guns, the use of a bicycle or similar conveyance, the use of a firework or similar material, or any other amusement or practice tending to annoy persons passing on a street or sidewalk.