Simple fact of the matter is that literally millions of people go into bear country every year and do not have any troubles with bears.

Yes you can carry a gun, however keep in mind that a younger bear, especially this time of year in good condition can run upwards of 30 mph. If you don't soon enough spot that bear charging you from 100 feet, do the math and figure out how much time you have to draw the gun, load then pull the trigger and hope that you did it in time. Same basic principles apply for bear spray...if not even less considering the relatively short effective range of the spray.

All in all though, the odds of actually being charged and actually attacked by a bear are extremely slim to none and I have never felt the need to pack a gun in bear country. I can think of a lot worse ways to be charged / attacked in an urban environment...