The Bull, like most stereotypical bulls, hates the color red, and it just so happens that Conker is a Red Squirrel. After Conker opened up the valve to release some Prune Juice, a target appeared which Conker had to make the Bull run into. Hitting the target opened a gate allowing Marta the cow to enter the Bull's field.
In both games his role is the same (naturally). Conker must first get him to run into a target to let the cows into the pasture. Then he must have him run into the target on the wall, upon doing so the bull will be immobile, allowing Conker to get onto his back to ride him. His controls are simple; the control stick steers him (though it is difficult), and B makes him charge. Once Marta is on the grate (taking a dump) the bull must run into her and kill her. The same is done for the other two cows (presumably Mavis and Olive, cows Marta has mentioned before), but once more than the last. After the final cow, the bull bucks Conker off and is left standing on the grate, which cannot hold him. He makes a reference to his weight (referencing Fat Bastard off the Austin Powers trilogy) and falls through the grate.
After Conker learns how to swim underwater, the bull can then be seen floating around underwater, dead.