It's a good discussion. My wife is a strong and experienced road rider. But she does not drink while moving. She believes that it's an unnecessary risk. I've never understood this, but I keep my trap shut and ask her if she'd like to stop and drink periodically.

The OP received good advice, which is to practice. Practice reaching down and placing his hand on the bottle. Practice reaching down and grasping the bottle. Practice reaching down, grasping, removing and replacing the bottle. Then add lifting the bottle to drink before replacing. Like all simple physical skills, this one has elements of core control, head control, eye control and general balance throughout. It's not too tough once mastered.