To compete in a pink slip race you must have unlocked at least 2 Extreme bikes in the single player mode. This is easiest to boost with another player where both have 3 of the required bikes and simply pass one back and forth (win every other race). At a bare minimum one player needs 3 and one can have 2... so long as the one with 2 wins first. Pay attention to your order or you'll end up playing single player again to unlock more bikes.Torchstone
just commented that this didn't unlock on completion of the 10th race. Be aware that an additional event may be necessary.