This is not a good place to be during thundershowers. The road can get mucky and the canyons are very flashy and potentially deadly.
Good approach shoes, and long pants and shirt you don't value highly are preferred for groveling in the slot canyons.
The San Rafael Swell can be OHV hell, so don't even think about coming here on a busy holiday weekend. Think mid-week, off-season.
The Behind the Reef road is a jeep road that is mostly fairly easy. It runs through magnificent desert scenery. And aside from its serious remoteness and some up and down, it's a non-threatening ride. Maybe that's what you are looking for.
The best reason to ride here, however, is not for the biking. It's for the access your mountain bike provides to incredible slot canyons slicing through the San Rafael Reef.
The first canyons--down to and including Little Wild Horse and Bell--can more easily be accessed from the Goblin Valley side of the Reef. But as you go further west and south, that road turns sandy and desperate. Before long, you are looking at pretty serious wheelin'.
So why not just drive out the Behind the Reef Road? Because while it is generally easy, there is a very difficult jeep section at Chute Canyon that prevents most vehicle access. This is a good place to park and start your ride, saving several miles and a lot of time, versus beginning at the start of the route where it leaves the Temple Mountain Road.
So, this route is seemingly designed for mountain bike commuting! Ride as far as you like, stash your bikes and hike down one slot canyon, across the reef and up the next canyon, then retrace your route. Good canyons to pair are Crack/Chute, Little Wild Horse/Bell, and Ding/Dang.
Little Wildhorse/Bell are the busiest of all the canyons, the easiest to access, perhaps the most scenic, and completely non-technical: you can take your (active) grandparents through these. Don't take your bike! This is a hiking trail, and there's too much sand to be fun anyway. There's also a section of narrows so tight that you'd have to remove your pedals and turn your handlebars sideways.
While there are a couple of frictiony down-climb moves in the other two canyon pairs, they are essentially non-technical (that is, if you go in the order suggested--down the first, up the second). You may want to bring a short hand line, though, just in case.
If you intend to go further out the road than this, you may want to camp at the start, and you'll still have to seriously beat feet to have enough daylight to finish before dark. The canyons also get more technical the further you go: there are some keeper potholes in some of these further slots, so don't do anything tricky unless you really know what you are about--people have died here.