Rib, felt, wool or cotton?

So…

I have this new drink bottle —

— and I want to knit a bottle cozie.

I’m thinking some kind of ribbing, so it hugs at the narrow part and fits around the wide parts. This idea eliminates making a felted cozie (I have a couple of cute patterns for those).

Perhaps an undulating ribbing…

The thing is, I want it to be absorbent, too.  Wool, then, or cotton??

Any ideas appreciated.