I've lived in Wyoming/Montana for the past 30 years.
Done a lot of backcountry riding in griz country and have had a few overnight "visitors".
It sounds like you are using safe camping techniques - make sure you hang high enough.
Also, I tend to have my smelliest meal for lunch - snackish meal for dinner.
Not sure whether you are heading N-S or S-N or when.
Also, whether you are doing the Canadian Rockies.
The risk is greater N-S if you are leaving in late May / early June.
Bears coming out of hibernation are hungry and more likely to be involved in an encounter.
Also, bears start the season at lower elevations - streams & lakes.
Just where cyclists like to camp.
That's why Yellowstone and other parks close such areas early in the season.
But usually such closures do not extend to neigboring national forests.
About ursacks - regulations vary according to land managers.
(Also, ursacks don't always meet backcountry requirements - check!)
As a cyclist, you cannot be in wilderness areas - where they may be required.
If you plan to do short overnight hikes into wilderness areas - then, yes.
In griz country, you should have sufficient trees for hanging - but not always.
I've had to bike lots of extra miles late in the day to get thru burn scars.
Also, in the desert areas critters will be attracted to your food.
Have a great trip!