Quote Originally Posted by redrhodie View Post
Move your hands toward the center of the bars, near the stem. You'll be more stable there.
This is good advice - this is how I get my bottle, I move one hand to the center. It feels much more stable that way. I also move my hand to the center when I signal and/or need to look behind me.

I also do the same thing Oakleaf mentioned with switching the bottles.

I try to avoid drinking when I know there will be potholes to dodge or traffic to watch out for. If traffic is heavy or the road is rough, and I'm very thirsty, I will pull over for a sec to safely drink. You definitely don't want to take your hands away from your brakes if you know you might need them