Players control a miner named Bounty Bob that has to claim every square of a mine while pursuing the evil Yukon Yohan.
The game, as originally developed on Atari 8-bit platforms, consists of 25 levels where players complete a series of jumping puzzles in order to claim all the land in a mine. Ladders, Slides, and Suction Cups are there to help the player along the way. Land is "claimed" by walking over it, which fills in lines on the various platforms that make up each level. When the entire level is filled in, the level is complete and play proceeds onto the next stage.
Bounty Bob will lose a life if he falls down or comes into contact with a mutant. Mutants can be made safe by collecting any of the irradiated objects strewn about the level, which turns the glowing mutants into harmless green creatures for a brief period. The nature of the collectable items and the limited time with which the player can turn the tables on the enemies are reminiscent of elements of Donkey Kong and Pac-Man.
The different ports of BBSB! made various changes to "fit" the game onto different hardware. The BBC Micro version, for example, has 20 levels.