Hook it

In case users would want to carry it around on them and not in a sports bag, here’s a solution. Suggested construction is of Elastomeric plastic so that it can expand and shrink enough to fit snugly onto the bottle.
Use the equipped snap hook to fasten anywhere, or attach a lanyard for slinging over the shoulder. The unique design of this bottle makes it appealing as a show-off piece; users may want to display it more than to stow it.
Integrated receptor for the hook could also be molded in as another option. It should be noted that if the hook is not used, the receptor may appear foreign to the user. This is, however, probably the least expensive solution.