Not so much a guide just a bit of help and advice.
You have to wait till you progress into the game and get to Golden Saucer.
Go to Wonder square and up the stairs on the right, then the bike arcade game is in the 2nd room at the back.
Basically with this you have to defend the car, like what you had to do earlier in the game.
I got it on my second go so it's not very difficult, every time the bikes bump your car you lose points so just stay back and try to hit them off before they even reach the car.
My tactic was to try and mainly hit to one side. I drove on the left and swung right also hitting right at the same time. Hope this helps :)
If you leave negative feed back please let me know why and be helpful :)