I live in New Brunswick were we have many Black Bears, like 1 per 2 square miles, but they are very timid. Attacks are extremely rare. No fatalities have ever been recorded.

That's still alot of bears though. Maybe you should check again. Chances are they are out there. Most important thing is to not tease the heck out of them with food smells. At established camp sites and in parks, follow the rules also. With small children, the risks are higher, and the loss is more dear, so you need to take extra precautions. I hike with a large stick, keep her close, don't use any lemon-flavoured bug sprays on her, and sleep with her in a tent. I don't carry bear spray in Southern New Brunswick, though I've considered it. In Northern New Brunswick, I might.

I carry a one pound hatchet also, when with my daughter. Sounds silly in summer, but its useful for tapping a small nail and splitting deadfall sometimes in wet areas, and I sleep better at night, as the big stick wouldn't work so well in a tent. Wouldn't work so well on a bear either, but most bears down here are small anyway. I don't know, but I think the main thing with children is that bears might naturally repect protective behaviour. Keeping them close, carrying a stick, and sleeping with a hatchet might improve my posture if nothing else, and hopefully that is enough for the bears to understand. Maybe I smell different with a hatchet. Who knows?

I think keeping the smells down is a very important step.
Bears can smell through anything, but its a matter of degree.
Out of respect, if nothing else, there's no sense teasing them.
I think a wood fire helps also. Doesn't need to be big.
A couple of uses of my Kelly Kettle is enough to leave a smoke smell.
Sometimes I make a small fire also if I need to dry socks and stuff.

p.s. I hang my food when in parks, or at established campsites.
When in remote areas I don't hang food unless I'm with my daughter.
I always keep the smells down though.