I grew up in the Cariboo Chilcoltin - that is dead smack dab in the middle of Beautiful British Columbia, Canada.
I grew up with waking up to see Black Bears in our yard munching on my Mom's Berry Tree's. I grew up hiking and coming across Wildlife of all sorts, and trail riding and camping and canooing and all those outdoor jazzy activities.
Trust me darling, a Black Bear will hear you before you hear it and smell you before you even know it is around. Majority of the time, the Black Bear will be gone before you even get to the area it once was.
IF you do come across a black bear, I guarantee you that they are far more scared of you, than you are of it - and once it realizes you are there, they will skidaddle.
The only time to be worried about Bears, is if you come across them with their Cubs, but again, most of the time the Mamma's will scurry their kids away to safety - but you get inbetween them, then you have something to worry about.
Black Bears are piddly compared to other species of Bears. Like the Grizzly - now there is a species to be worried about, but Black Bears are nothing.
Now IF you do get into a situation - and this will be a VERY rare occasion if any at all - DO NOT RUN!!! BIG #1 mistake. STAND YOUR GROUND. IF the bear stands up on it's hind feet, they do this to make themselves appear bigger, you - do the same. Make yourself look as big as you can - the tricky part, is your horse. BE LOUD, if you can, carry an Air Horn with you, in a fanny pack or a small backpack - and blast it. Scream, roar, wave your arms. BUT DO NOT RUN. NEVER RUN.
IF you are worried, do what we all did back home - put bells on your saddle. Not little rinky dinky bells, but those big one's. Go to an Outdoor's store - where they sell camping gear and bear spray and outdoor gear tech, etc, etc, etc - and ask for Bear Bells and they will know what you are talking about.
The bells are your best bet to keep people who are not accustomed to seeing Wildlife, mentally sane.