Add a loop of line to the neck of your bottle, possibly with a clip on the end. That way you can hang the water bottle from anywhere on your clothes or your pack. Moving the bottle from your water bottle pouch, backpack or whatever will free up valuable space for other things, including tinder or firewood that you find on your way.
The bottle is easier to access (= more frequent sips), which is good, but will dangle, which may or may not bother you.
I wouldn't put duct tape on a steel bottle if you plan to boil in it. You then either just let the duct tape burn/melt or you remove it. Unrolling duct tape is a hassle and could possibly render it useless if you're not careful to roll it onto something else. The last thing I need in a I-should-boil-water scenario is the mental barrier of removing and possibly destroing my precious duct tape, which is a resource I'd want to keep. Obviously, if you go the bottle-in-a-pot route this isn't a concern.