I've got the Olicamp cup with my 1L Nalgene, but they're together in a Cordura belt pouch made to fit the bottle. I just use it as a canteen, though.

There are several brands on the market, some even insulated. This one (don't remember the brand) has delta-rings for a shoulder strap, a belt loop, & a drawcord top. They're available in numerous places for $10.00 or less. I keep a spoon in the cover with mine, too.

Even a few thinner turns of tape would provide a good friction fit, too. I had not thought of the rubber band, or bandana...great ideas.

Thanks.

David