How are things up there?
I've found the following sources of information on road access to Verde Hot Springs to be helpful.
Coconino N.F. Red Rock District road closure alerts | https://www.fs.usda.gov/detail/coconino/alerts-notices/?cid=STELPRDB5341633
Roads you need to check: FR 502 and FR 708 (Coconino side)
Two phone numbers which may also provide Verde H.S. information (in the unlikely event the above webpage is unavailable):
Fossil Creek hotline recording 928-226-4611
Red Rock Ranger Station 928-282-4119