Bob had a straight to the 8 and Alice had a straight the 8, Bob had a 4 & Queen, Alice had a 8 & Jack. Who wins?
Assuming you mean in Texas Hold'em (which you should probably state), then they tie. In Texas Hold'em, you make your best five-card hand out of the seven cards you have available to you. It sounds like from your description that Alice was holding
and that Bob was holding
which would mean that the board had to have on it (since both of them had a straight to the 8)
4 5 6 7 8
which means that the best possible five-card hand that both players could have (in fact, that any player could have*) are the five cards on the board. As such, all players tie.
Essentially, the J/Q in that they are holding aren't even part of their hands when it come to determining the winner, and so are irrelevant.
Edit: * Well, that's not completely true. If another player were holding a 9, or a 9 10, then they would have a straight that was 9 or 10 high, which would obviously beat an 8-high straight.