I guess I'm getting old but the best "bike game" ever was Paperboy! It was actually an arcade game with handlbars as controllers. Paperboy was ported over to every major home console during the 80's and early 90's. You could get the game on the Commordore 64, IBM PC, Apple II, Nintendo Entertainment System and Sega Master System.

The object of the game was simple. All you had to do was throw the morning paper by the doorstep of paid subscribers. You received extra points by hitting burglers, drunks and breaking the windows of nonsubscribers. All this while avoiding cars, cats, dogs and angry nonsubscribers!

What a game

P.S. You can still play the original PaperBoy using the Mame emulator.