Practice with both hands - and be aware of how much your weight shifts if you have to pull to get the water bottle out of the cage, and work on holding your line.

Be aware which hand and brake are available while you're drinking. I like to try to keep my hand on my rear brake, rather than the front - so I'm using the left hand to drink.

The only thing for it is practice, practice, practice. Learn to feel the top of the cage with the bottom of the bottle, so you don't have to look when returning it. Also keep the bottle exterior & cage clean so it's not gritty and sticky when removing the bottle.