Another thing to try doing is practice without actually removing the bottle. First just practice removing one hand from the handlebars while the other hand is closer to the stem; next try reaching down for the bottle but not removing it. That way you will get used to riding one-handed but not have a bottle in your hand if things go wrong.

I've used my right hand to reach for a bottle for the 10 years I've been riding. I've lately been trying to practice using my left hand more -- it's hard!