In other words, how long before bears learn that it's pointless to raid campgrounds?
This particular scenario fits in the category of "behavioral extinction". Having once learned that campground = food, how long does it take to unlearn it?
It depends on several factors, most notably the frequency of reinforcement of that lead to the learned behavior (campground visits) in the first place. The hardest behaviors to extinguish (unlearn) are those created by variable-rate reinforcement, where you have to keep trying again and again to get a reward that doesn't come on any predictable schedule. (Slot machines work on this principle.) If the bear is used to finding food on one of twenty visits to a campground, he can be expected to visit at least twenty more times (probably forty) before he figures out that something's changed. Since "one in twenty" is an average and not a predictable schedule, multiply that by several times - the bear has no way of knowing he's not just having an unlucky streak.
The harder a bear had to work before for free food, the harder he'll keep working before he learns it's gone. If he'd been getting a handout every night, he'd probably give up in a week (though he might try again once or twice later). Getting a handout about once a month on no particular schedule - likely to keep trying for a year at least.
Bears surely understand that camper-food is a seasonal item, like blueberries, so time elapsed in the off-season won't count.
In the real world, as opposed to the lab, availability of other food sources plays a role too, though I suspect that blueberries and other easy foods aren't nearly as tempting as marshmallows and steaks.
