Ruling: Entrance cards with Start of Match effects will always trigger before the first Turn Roll of the game. 

If you win the first turn roll the opponents entrance is blanked for the rest of the match.

A bump is a Turn Roll, and will count as the “If Not” clause. This effect will carry over to your first opponents turn, even if you win the next turn roll after the bump. If your opponent stops your first card in this case, they have utilized Jumps the Bell.