I have this water bottle. I use it a lot, but it's ugly. I like cold drinks with a lot of ice, but they tend to leave puddles on tables and counters. This makes my husband growl.
None of these are a problem any longer, though. The answer to my problems were just in my sewing closet, awaiting a moment of inspiration - the Sleeve:tutorial I used referred to the slightly odd shape of a fountain drink cup, but I modified mine to fit my straight-sided bottle. It was also easier because I used some scrap felt inside, rather than quilt batting that needs to come between two layers. I like me some shortcuts.
I'm thinking this would work not only as an absorbing tool for cold drinks, but an insulating one for hot drinks as well. I'm sure it wouldn't be too hard to modify further for to-go mugs or even a large thermos. The possibilities are...quite a few!