A single coyote is not a problem. If you are concerned, get off the bike and put it between you and the coyote (same as for a barking dog), they have no idea how to handle the bike.

A hungry pack, ride as fast as you can.

My guess is that this coyote probably had a couple of pups in the bushes. It let you follow it while it was leading you away from her pups, and would have eventually ducked into the bushes and circled back once she felt you were far enough away. The fact that you turned back, heading back towards the pups concerned her, so she followed (and might have put you in danger if she felt the pups were in danger from you).