Welcome and good morning!
I have a old H&R 12Ga I use as a camp gun too. I like it because it is a take down model from the early 1900's. But I have to say, its more for the two legged varmints or the kind that harass the chickens or climb in the garbage cans. If I knew Bears where the issue, a beloved H&R SS would be about the last choice I would consciously make. I realise its far better than nothing, but it sounds to me like you would be entering into a situation expecting a confrontation. Personally, I would avoid this scenario. If it was mandatory, one of my Remington 870 would be a first choice.
OK its your choice, I offered my opinions... As for a site on such a firearm. Open sites definitely! If you will be staking life and limb on something, it better work every-time NO QUESTION. That 870 of mine wears a custom rear peep that is very sturdy, it adjusts with "meshing teeth" and held to the receiver with weld and the peep adjusts with two screws. You could beat it against a wall and it would not move. The front site is welded to the barrel. Making it almost as sturdy.
Small fixed scopes can be mounted and quite durable. Many African hunters use them on "stopping rifles" for BIG dangerous game. But if you really look, most all PH's will have open sites and a double rifle. Personally, when I look at the ranges associated, peep sites are all that's needed. Both eyes open, instant target and site acquisition is a must. A scope would be slower, maybe just a little, but a little may make all the difference.
I have a set of XS sites on a 375 Marlin and like it very much. The sites are well made and sturdy.
Good luck with your choices,
CW