OP, ride an relax. Don't over think, just be alert. I retired to a beautiful national forest west of Glacier National Park. I live between 2 grizzly and black bear habitats. We also have mountain lions. This doesn't keep me from riding the unimproved forest roads in spring, summer and fall. (Exploring the forest by bike is so rewarding. Everywhere you look you see spectacular views like the one below.) I stay alert to my surrounds (in urban/suburban areas, you probably need to be as alert about the humans surrounding you, you're much more likely to be injured by another human, intentionally or unintentionally). Here, given that we have grizzlies, it's not recommended that you carry pepper spray without being taught how to use it. The best way to stay safe is avoid an encounter by being aware of your surroundings. And noise doesn't necessarily deter a bear. I hope never to have an encounter with a bear, either grizzly or black bear. (I don't want an encounter with a mountain lion either.)
