I would encourage you to take seriously Lisa's advice about protecting your food (and yourself) from bears while camping. We spent many years car camping and backpacking in the Colorado mountains and securing food was always a high priority. It's a lot harder when backpacking--you have to rig up a rope around the food container and haul it up between 2 trees--but it was possible to do without too much trouble. Put all your food back in the cooler and put it in your car at the end of the day. Take your garbage to the campground dumpster, which should be bear-proof, every night. Don't leave any food lying around your campsite while you're off hiking. Not only might it encourage a passing bear to come back later but it could attract dogs or other critters who would have no shame in snatching that bag of potato chips off the picnic table.
That said, unless there are bears who have become accustomed to raiding trash cans in the area, you shouldn't have anything to worry about. In fact we've never actually seen a bear in a campground or back country site. We now camp, princess style, in a small RV so we aren't as rigorous about this as we used to be. As I told my husband, I'm too old to sleep on the ground anymore.
Have fun with this. It is wonderful to get away from the lights and sounds of the city. I assume you'll be doing this when the weather warms up. Winter camping is not for the faint of heart--we only did it once and did not enjoy it.
Nancy in Pátzcuaro