The Vincent

The Vincent was Billy's motorbike, which had a passenger sidecar. In 1959, he used it to take Delta and the Chimeron princess to a beauty spot, and later lent it to the Seventh Doctor, who used it to parley with the Bannermen and rescue Melanie Bush and Burton. Billy gave the Vincent to Rachel Defwydd when he left Earth with Delta. (TV: Delta and the Bannermen)

Behind the scenes
On screen the model is not specified, but the Vincent was actually a rare Vincent Black Shadow. This was the exact bike that features in the original script. (INFO: Delta and the Bannermen)