Thanks for reaching out! This is a really good question, thanks for bringing it to the community. @Dad_Aint_Hip definitely gave you some great advice, I'm going to add a little bit from my own experience.
Having lived in Alaska, I can speak with experience to the ever-present danger of (very large) bears. I have traveled in the backcountry with and without firearms (I do not own one either, however, many of my adventure partners did) and had the good fortune of never having a bear encounter where I feared for my safety. I attribute this mainly to a very healthy fear of bears that drives me to take all steps necessary to prevent a negative encounter (for my own life but also for that of the bears).
When traveling in bear country I always make sure to bring three things:
1) Knowledge. This is usually gleaned from the friendly rangers in whatever jurisdiction I'm in. I'll ask if there have been any bear sightings or encounters, what are the requirements/suggestions for food storage (it could be that a bear barrel is required), and if there are any restrictions for carrying a weapon or bear spray.
2) Bear spray and a holster. From the years I spent in Alaska I had this on me at all times when I stepped onto a trail in the backcountry. The holster allowed me to place the bear spray on my shoulder straps when using a backpack, or my waist belt when cycling (I always wore a fanny pack). Additionally, I ordered some inert bear spray canisters from Counter Assault to practice with. While not a complicated system, I found it reassuring to know what it felt like to fire off a canister and exactly how far the spray shoots. It also is important to remember that the idea is to create a cloud of bear spray that the bear charges through and inhales deeply. That helps create the kind of reaction that has the bear heading in a different direction. It is really important to know your surroundings and, most importantly, how the wind is behaving before deploying bear spray.
3) Bear bells. These are fiercely debated as to whether they are effective or not in alerting bears to your presence. What I believe is that if I'm afraid of bears enough to use a bear bell, I'm going to be afraid enough of bears to take all the appropriate precautions to keep both of us safe in the backcountry. The bear bell also serves as a nice reminder that I need to holler 'hey bear' one more time or come up with another song to sing on the trail.
For me, bear spray is a much easier and less expensive way to prepare for a bear encounter than a firearm. Not to mention that the threshold for a very bad outcome is much lower if something goes wrong or a mistake is made. I will mention that there are restrictions on bear spray in some places (some states consider it a firearm) so you'll want to make sure you are checking regulations for every place you go.
Lastly, I encourage you to check out these Expert Advice articles on safety in the wilderness, they contain a lot of good information on many related topics as well.
Hopefully this helps, thanks!