There was an air and ground search after two men in one of the vehicles ran off following the crash in the High Street.
An Avon & Somerset police spokesman said: “Officers were called just before 10.20pm by reports of an accident involving two cars which had partially blocked the road. The two male occupants of one of the vehicles made off on foot.
“A couple in the other vehicle, while shaken, were not believed to have been badly hurt.
“A search of the area, including the use of a police dog, led to the arrest of a man in Willsbridge.
“A 20-year-old man from Bitton arrested on suspicion of failing to stop at the scene of an accident, dangerous driving and driving under the influence of drink or drugs, and was later released on police bail, pending further inquiries. “
Anyone with any information is asked to call the police on 101.