As for bears they are there. I never encountered one close up though, but of course YMMV. I always hung my food up if there wasn't a bear box. My basic procedure is to take precautions but don't stress about it.
So I'd go North to South. First off the maps are setup that way and while ACA always makes a token effort to do the opposite direction the maps are just not as useful the other way (for instance the elevation charts only have the distances from left to the right in the "preferred" direction. They easily could put at the top of the chart the distances in the opposite direction but they chose not to). Secondly the mountains and passes get higher and higher from North to South. Just starting out before you get acclimatized to climbing a pass every day (and you will, sometimes more than one) it is better to have the lower climbs. Thirdly the heat. It gets really hot in SoCal (record temps right now for instance) so it's better to start in the north where its cooler. It does depend on the time of year and such you are doing it. When I rode it, I was often hitting 90 - 100 degree (F) days in the San Joaquin. I chose not to ride the final map (starts in the Mojave pretty much) due to the heat and reports I'd gotten that a number of the campgrounds had no water. All the locals recommended spring or autumn for riding the Mojave/Joshua Tree area not August/Sept. which is when I was there.