To jump as far as possible, activate the turbodrive just before reaching a ramp. Rear up on the back wheel, and then press forward in midair to straighten the bike. This will take you further than if you would jump while rearing. Try to land on both wheels at the same time to lose as little speed as possible.
While not the fairest of moves, tripping your opponent is pretty effective. Move halfway in front of the opponent, just above or below him, so that your back wheel is lined up with his front wheel. Then move up or down, so your back wheel goes intohis front wheel. He should trip, and you should come out of it ok, IF you do it right.
get up fast:
To get up fast after falling off your bike, tap A, B, A, B rapidly. This will make you run to your bike faster than if you just wait or jam on the same button.