It took a while for me to develop that skill.
Practice in safe places - on nice, flat, straight stretches maybe in a neighborhood as opposed to the road so less traffic. Try riding one handed for stretches of time to develop the strength and steering capability of that arm. Don't try to get your water bottle while riding until you feel comfortable riding one handed for a little while.
Do it in steps.
Glance down quickly, see exactly where your hand needs to go. Look back up!
Reach down while still looking ahead and get your water bottle. Hold it, make sure you are balanced.
Take a drink. Make sure you are balanced.
Glance down, see where it needs to go. Look back up.
Reach down and put it in the holder.
I ride with one friend who has been riding a little less than a year and only drinks when we stop, so you are certainly not the only one! It will be second nature before you know it.
Grits
2010 Trek 5.2 Madone WSD, SI Diva Gel Flow
2002 Terry Classic, Terry Liberator