I also wouldn't walk my dog unleashed. But, she loves going on bike rides with me. She gets really excited when she sees the bike and leash. I walk her to the nearby park, about 2 blocks away, once there, I take her off the leash. After a couple of warm up laps, I start to go faster so that she can run.
After the run, I usually put her back on the leash and we go for about a 2 mile ride at a slow speed. The speed is about a trot for her.
This took a lot of training, but I now have her trained to stay at my back wheel on the right side. She knows "left" and "right" for when we turn, "slow down" and "stop". I have also trained her not to go after squirrels. She is very well behaved with the bike, but I still wouldn't allow her to go unleashed when on the roads.
As for water, I had an old soft sided cooler that had a bottom section. I cut the bottom section off. It works great. It holds a little over a water bottle amount. I fill her bottle up and place it in the cooler section. It is a tight fit, but I can get it into the bottle cage. I stop to allow her to go potty and drink when I think she needs it.
Walking a dog on a bike is great. I have arthritis in my knees and it is painful to go for a couple of miles of walking, but I can ride a bike all day. Also, with the speed, she gets a much better workout.