This pattern will make either the smaller demi cozy that will cover the bottom of a coffee cup or a larger tote-style bag for a water bottle. Or you could make one (or more) of each.
The pattern starts at the bottom, first making the base and then working up and around the body of the cozy. The crocodile stitch gives the piece a scaly appearance. Then there is a choice of strap--either a long strap with which to carry the cozy over a shoulder or a short strap that will fit over a thumb or finger.
The yarn used in the demonstration photos was Loops & Threads Impeccable, but any worsted weight yarn will work nicely. A full skein won't be needed, and the demi cozy can be completed with odds and ends.
The pattern is written for a bottle in the 20 oz range or a coffee cup with a 3 inch diameter at the base. However, the crochet gives a little, and with a change in hook size or yarn size, it can easily be made a bit larger or smaller as needed. The instructions for fit are in with the instructions for gauge and the making of the base.
The pattern is written out and illustrated with photos. The final file ends up at 24 pages.