Yes! For trails check out https://www.mtbproject.com/ and https://www.hikingproject.com/

Tons of great hiking trails and off road 4or trails. Not sure about biking.

There are all kinds of places. We went to Devils Bridge where they have biking and hiking trails.

This is a cool “Travel Map” (off road, etc., map) for the USNF’s in the State of AZ. Be sure to “update the map” https://www.fs.usda.gov/Internet/FSE_DOCUMENTS/fseprd725291.pdf. Happy Trails

All the trails near Forest road 525 are ATV trails so while it is possible to mountain bike it is not pleasant due to the ATV traffic and dust. The closest actual mountain biking off of Boynton Pass road heading from the dispersed camping area east towards Sedona. Start at the Aerie trailhead. Do NOT try to Mountain bike from the Devils Bridge trailhead because all you will do is dodge hikers, ATV's and dust balls! From the Aerie trail head you can go north (harder biking) or east (easier) on the Cockscomb trail. Cockscomb will connect to Aerie trails (left - to make a loop.) Or go strait a the Rupp trail and Girdner (or Two Fence) will take you east into West Sedona near the Lizard Creek trailhead. Signage on these trails is pretty good but sometimes hard to read because of sun fading on the signs.