You know, I was worried about this as well, until I went riding on a really hot day and I was forced to just grab the water bottle, drink, and put it back. It was either that, or dehydration and feeling dizzy. What helps for the first few times is if you slow down a bit (stop pedaling, or pedal slowly) to reach down with your hand and grab the bottle. Oh and also make sure the road isn't too bumpy.

It gets easier over time!

Next thing I want to try is pedaling without holding on to the handle bars. But I think that won't happen anytime soon!