Another option to consider is taking Bloody Basin Road (Exit 259), which is roughly 25+- miles (North) from the Table Mesa Road exit and about 15+- miles from Bumble Bee Road. Make sure to head west of Interstate 17 along this dirt road as it will eventually lead you to Bumble Bee Road (and the exit I mentioned yesterday). The trail is very driveable in a 2WD vehicle, takes about an hour and offers plenty of open desert to find a suitable spot to park your stuff.
There are two major forks along the way and you’ll want to take a left at both. I believe there may even be signs indicating their destinations.
At the first fork, DO NOT head to Mayer, as it will lead back to a highway.
At the second fork, steer clear of heading to either Crown King or Cleator, which head into the Bradshaw Mountains. While those areas are fine to explore, staying lower will help you find a convenient spot to set up and remain closer to Interstate 17. This area is popular with hunters and generally free of the issues seen west of Table Mesa, such as littering or disruptive groups.
Once back on the highway, the area is no more than 20 minutes from Table Mesa Road. Hopefully, these directions are clear and helpful.