+1 on breaking down the action into it's smallest parts. just riding with one hand, but not going for the bottle. Then riding with one hand and just trying to touch the bottle. Progressing up to removing the bottle just a touch and pushing it back into the holder, etc. I was riding for a year before I figured out how to do this. And I started out, just drinking when I was on a piece of road where I could coast without pedaling. I got the bottle out and drank while coasting and just steering with one hand. Worked my way up to pedaling while drining.
So, take baby steps. The worst thing you can do is allow yourself to get dehydrated on the bike!

