The general feeling was that fast predictable movement does not offer much defense, and unpredictable movement is handled by dodging.
To be honest, that was my feeling as well.
But when you're on the ground and trying to hit something moving, you have to predict where it will be in the near future, and it's not as easy as it seems. And actually, I think that the further away the target is, the more difficult it is, and bows, crossbows and slings are not lasers - the projectile does not reach its target "instantly".
Or, to put it more plainly : at a given range, it's more difficult to hit a moving target than a stationary one, even if the target is not actively dodging. And the more it moves, the more difficult it gets.
So, despite my initial feeling that this should be handled by dodging, I would actually give a DB bonus for speed (given that range is already taken into account in modifiers), *on top of* any avoidance you can have from activity besides simply moving. The only exception would be if the target moves towards (or directly away from) the shooter, because in that case, you don't have to predict anything, just shoot straight - if the target avoids the projectile, it is because of dodging, not because you miscalculated the point of impact along the target trajectory.