When I toured with my daughter and one of her former college room mates, they did something similar. They used a cheap replacement water bladder complete with hose and bite valve ($8 from WalMart). They put it in the front pannier and had the hose run up to the handlebar. They had to bend down a bit to drink, but found it worked very well. They would fill it with ice and water and even in 100+ F heat it stayed cold a long time. The only drawback was that it was hard to judge how low they were on water until they ran out. Since they also carried bottles they used the bottles last for that reason.

On the bottled vs distilled vs tap water issue. I alway drink tap water unless it tastes really nasty, then either filter or resort to bottled water. Since I prefer not to carry a filter that usually means tap or bottled water only. In the US I just take my chances that the tap water is safe.

I think that distilled water tastes AWFUL. I guess that if you added the right minerals it might be OK, but when we bought it by mistake we found it almost as bad as the really bad tap water we were trying to avoid. We wound up using powdered gatorade mix so we could stand to drink it. It is hard to stay well hydrated when the water tastes bad.