It's the desert- no bears.
I have seen a small black bear swim across the river and up the bank at the loma putin for Ruby-Horsethief. In addition, there was a black bear bite on the salted-dreadlocks of a sleeping hippie on a NOLS course 2 summers ago on the Deso-Grey section of the Green, which is most definitely desert. Probably thought the hippie's dreads were a salt-lick. Statistically black bears are way more likely to look at humans as prey these days than grizzlies, but the chances of being attacked are tiny. Practice good bear etiquette (the hundred yard triangle of cooking, storing food, and camping upwind of these) and you should be fine. Also, carrying a shotgun or '45 or '44 (better yet) is the best protection. Bear spray sucks. I know that bears run 35 miles/hour, which translates to about 60 feet/second (actually 51.333'/sec.). If a bear charges, that leaves you 1/3 second to get the bear perfectly (max range for bear spray is 20'), and is dependent on perfect environmetal conditions: open range, good light, and correct wind direction. A slight shift in wind and you hose yourself but good, which in my experience is no fun. Better than nothing though.
Also in my experience, even gun grabbers are quite happy with the knowledge of that existing protection when the bear actually comes snuffling at your tent door, and are more than happy to eat their words of protest, until the next morning when the bear is gone, and they feel safe again, and the protection becomes once more inherently evil
Have a good trip, and count yourself lucky to actually see a bear if you do.
Cheers and beers,