"Do the bears push the smaller preds out?"

No. While they wont be standing side by side sharing a meal (LOL) Coyotes and bobs are FAR too quick and agile to care one way or another about a bear in the area. Ive also been to a few areas that hold good numbers of all three.

bobs and especially yotes have large territories and its not at all odd to see large amounts of sign in an area for awhile and none at all on later dates.