Hi all,
I'll be installing a set of non-ergo cork grips onto a bar this weekend, and would love to get some recommendations on what type of adhesive to use. The grips slide/rotate freely as is, so I know that some form of adhesive will be necessary.

Hair spray or artist's spray adhesive. Three coats of shellac (on the outside surface) will keep them looking nice.

Wrap the metal bar with electrical tape, the friction between the cork and the tape as well as the slight increase on diameter will keep the grips snug. Soapy water or alcohol hand cleaner if you need a little lube to slide the grips on.

I think Jeff Jones recommended 3M Super 77 spray on adhesive for mounting the cork/foam grips to his bars. I bought a bottle of it at Home Depot years ago, but still haven't gotten around to using (infrequently ridden bike).

Bingo!
I have the Jones loop bar, so will heed this recommendation.
The bike will be seeing daily (all season) commuting use and will also see weekend duty on singletrack and potentially multi-day bikepacking adventures, so any form of movement is not an option.

I used Gorilla glue. It was perfect for 3 years, then I sold the bike. I assume it's still holding up fine although it would probably require sanding to remove it when the grips fail.