These bike colors are unlocked when you get all S Ranks in the 4 cups.

Color	How to unlock
Electric Blue	Get all S ranks in the Platinum Cup.
Forest Green	Get all S ranks in the Bronze Cup.
Lemon Yellow	Get all S ranks in the Bronze Cup.
Plum Crazy	Get all S ranks in the Silver Cup.
Sea Green	Get all S ranks in the Gold Cup.
Skull	Get all 16 S ranks from the 4 Cups.
Speed Green	Get all S ranks in the Silver Cup.
Sunset Orange	Get all S ranks in the Gold Cup.
Void Black	Get all S ranks in the Platinum Cup.