If you are going for a backpack, look in places like REI

Doesn't have to be a bike backpack.

You can also get waterproof covers to put on just about any back pack. The down side is the part that lays against your back is still exposed to water dripping down your back. That can be mitigated with a hand towel placed in the back of the bag to give you a barrier layer.

And you can spray water proofing on them to further protect contents.

Obviously a fully waterproof bag is going to do a better job. But if you're on a budget you can reasonably waterproof just about any bag for about $30 in materials (cover and can of spray waterproofing)