I have hiked the John Muir in Yosemite, across the Grand Canyon a half dozen times, in the backcountry of Yellowstone, Glacier, Banff, and Jasper - Denali, Kluane, Wrangell-St. Elias and never had any problem. And not just a two-hour hike, either - 3 sometimes 4 days.
Maybe I'm just lucky. First, my bike is an older model - 1988 Trek 8000 adapted for touring. I use a basic cable and lock. Second, I use panniers. In bear areas I hang them a short ways off the trailhead. Clearly they are visible to hikers, but they have always been respected. Many trailheads have outhouses with sloped roofs and small rafters underneath. You can always hoist your panniers up into the rafters and make them less visible - I've done that a few times.
Machka is right about asking people at campgrounds - that is, if there is a campground near the trailhead. Another campground option is to leave your panniers in a bear box - provided that they are not heavily used. My experience is that most national parks in the U.S. and Canada have ample bear box capacity. I do not think that park rangers would take kindly to your locking the bear box, however, since they are public use.
Finally, I never have anything left behind that I cannot absolutely do without. Wallet, passport, camera all go with me. It would be a bummer and a big monkeywrench in my tour if my stuff got heisted, but I never worry one bit when I set out to hike.