Push bike - well if you wanted to do it properly, finish all 16 levels of the Crazy box, and it will
be unlocked for all characters, however, if you cant be bothered.....
At the character selection screen
press and hold L1 and R1 then release L1 first and then R1 . Press and hold L1 and R1 again but this time release them at the same time and press X. You will hear a ringing bell as you mount the bike if entered correctly.