Shewie,
I live in Northern California and do a fair amount of long distance backpacking here. Also I lived in Alaska and did the same. So I have a LOT of experience with both black and brown bears in North America -- including lots of experience with bears in some of the hot spots for rude bear behavior.
First off: a bear siting is thrilling and I *hope* you see several. (Years ago I did about a 60 mille backpack near Banff and saw about a dozen bears, but that was in the 1980s, so I don't know what it's like now.)
The reason I preface my remarks with saying I hope you see a bear is because that's the mindset that's best to have: eager anticipation is better than fear.
Sometimes you run into people in bear country here with chains of bells and multiple cans of bear spray and god knows what else because they're so frightened of seeing a bear. They're overwrought about it.
Don't be. You are less likely to be hurt by a bear even in a place like Yosemite (the poster child for bad bear behavior) than you are being hit by a lightening bolt in a thunderstorm. Acquaint the missus with the statistics and it will make her feel better.
That said, here are a couple of things to be aware of: always cook sixty or 100 meters from your camp. Do not have snacks inside your tent (I break this one regularly even in places this with black bears and only had two visits, both fled when yelled at.) NEVER deliberately feed the bears (I realize you know this but it must be said).
Hanging food is almost generally a bad idea. Even if you do it right -- hang a long line in between trees and then hang the food in between -- the odds are you're going to lose food to either a creative black bear or a racoon (brilliant animals) or even squirrels.
The better approach and the one most people use (it's a law now in some places in the West) is to put your food in a bear proof canister. These are large lexan plastic canisters that the bears can't get a purchase on. They actually test them with bears that are so bad they've been placed in zoos to get them out of nature.
They form a really reliable (and helpfully odor suppressing) container for food. Keeps out racoons and other varmits as well.) The can be expensive: US $75, but most places with bears have a spot where you can rent them for a few dollars. Canisters are better for the bears (they realize they can't get food from people) and for you.
Now, on the issue of bear encounters: brown bears (Grizzlies) are one of the great forces in nature and I *pray* you get to see a few. There used to be loads of brown bears around Banff, but I don't know about now.
Admire them, do not fear them. Grizzlies almost never attack people (when they do, it's generally fatal) however they will bluff charge from time to time if they feel threatened.
In my experiences -- maybe 50 close encounters with Grizzlies and a few hundred long distance viewings -- I've never been bluff charged. (I did have a Grizzly attack my volkswagen in Alaska, but that's another story -- it felt threatened because I almost hit it at night on a dirt road -- wild experience...)
If you get a bluff charge, hold your ground -- do NOT run; running triggers a predatory response -- but don't be aggressive in turn. Slowly, sedately move off. A friend in Alaska had a Grizzly bluff charge him three times and he said staying calm under those circumstances changed his life forever because he said he knows he can control his fear.
If Grizzly does attack, it's almost always because it feels threatened and if you cover up (especially the back of your neck) and lay still it will bite you and bat you a bit and go away. If an attack lasts more than a few minutes -- or if it starts to drag you more than a few feet (they hide their food, if they drag you it's BAD) -- you'll know this is predation behavior and it's time to fight for all you're worth.
Grizzlies almost never predate on humans, however. Statistically it is super rare.
Also, the odds of you running across a Grizzly by accident on the trail are miniscule. They stay away from people as much as possible. They're shy and beautiful. I love them. There are few things in the world cooler than a grizzly.
Black bears (which can be brown in color, FYI) are much smaller than brown bears and can be curious pests. They're VERY smart and VERY curious. Just as you never threaten a brown bear, if a black bear comes close you take an aggressive stance with them. Make noise, throw rocks. etc.
Ninety nine times out of 100 they're flee immediately.
Usually, particularly in areas where they've got human food, black bears want your food. If you have none they can steal, they move on.
However, black bears are known to predate on humans from time to time -- usually sick ones and even then it's very rare. Black bear predatory behavior is pretty easy to spot. If they follow you at a distance for any length of time, they're evaluating the situation. It's time to be super aggressive with them.
I've had this happen to me on about half a dozen occasions -- always young bears in the far wilds of Alaska, trying to figure out what I was -- and it's generally over fast and makes for a great night's tale around campfires.
If the bear is old and exhibits this behavior, you might have a real problem on your hands. It almost never happens, but.... With black bears you NEVER stop fighting. If cubs are not involved, a predatory black bear isn't attacking you because you're a threat it's attacking you for dinner.
(By the way, in my experience the mom and cubs thing with black bears is pretty funny -- the moms run like hell and leave the cubs behind to catch up. The mom and cubs stuff with Grizzlies is different though -- but mother grizzlies make a point of keeping their cubs far from where you will be...)
Also, if the any bear tries to come into your shelter at night and you've got no food, it's an alarm bell and you should be aggressive.
Oh, and scat -- black bear scat looks surprisingly like very dark human scat (check it with a stick, if you notice food wrappers in it, you'll know you've got a pest bear nearby even if you're in the far bush -- they relocate bad bears far away...) Brown bear scat tends to be much larger and often fairly loose.
Most of the time, the worse bear offenders are not where you are: if you're 10 miles from the nearest garbage can, the pest bears aren't there... they're in town working on the garbage...
One weird thing is happening in the West right now -- because of encroachment and climate change, some top tier predator behavior is changing. Increasingly mountain lions -- a super rare site in days past -- are showing up closer to towns and places where people are. So some behavior is changing, however, after lots of time in bear country, I assure you their behavior is pretty predictable.
But still my best advice: pray to see a bear. Get yourself a canister and rest easy, nothing bad will happen. They're wonderful animals and, other than the pests, they have very little interest in you.