Description taken from Arcade version of this game

The game's premise is simple: from a bird's eye perspective, race your vehicle against the clock to complete the course in the alloted amount of time. Along the way you will be faced with multiple obstacles. Not only will you be joined on the road by dozens of other cars who will attempt to knock you off, but you will also be faced with stretches of road that can't be crossed by conventional means.

Luckily your car is equipped to bump and jump, as the title implies. Use your car to knock the opponents into the side walls or force them into a dead end. When expanses of missing roads exist, once a certain speed is reached, you can jump over these roads. If your timing is correct, you can even use the jump ability to land on other cars for bonus points.

Bump'n'Jump is a clone of the original Burnin' Rubber by Data East but published by Bally/Midway. ~ Paul Biondich, All Game Guide