Well, you sound like a backpacker. I know, because I have done a lot of backpacking, and that was one question I had prior to doing the Northern Tier last summer.
Biking is different. I usually filled my water bottles at gas stations and stores along the way. Never needed to fill from a stream or ditch. Although I carried my filter, I never used it. So, my advise is to look at the map, and figure out the distance between towns, and how long it's going to take you to get there. Then, how much water are you likely to need. Myself, I carried 2 water bottles on the bike, and a collapsable Nagene Canteen. When it looked like I might need extra water, I filled the canteen. And this was not frequently.