It is not 100, it's 75 as mentioned in the Set Bounties privilege page:

At 50 reputation one gets the Comment Anywhere privilege, so the Set Bounties is between that and the three privileges given at 100 rep. Makes sense for me.

At 50 reputation one gets the Comment Anywhere privilege, and at 100 there are two: Create Chat Room, and Edit Community Wiki.

So to add extra "level", they decided to put it in between.

Another motive is that one can't have reputation of 0. If we could start bounties with 50 reputation, it means we'll drop to 0, which is impossible. And awarding the privilege at 51 reputation would mean dropping to 1 reputation, which is too low, losing all privileges in one go.