Well seeing as how we have absolutely no leash laws in my rural part of the county I deal with dogs daily. I have had one scary encounter going up a hill which I was saved by a motorist cutting the dogs off.

Other that I have decided the real danger is hitting the dogs, not being bit. Most of the dogs around here come to a screeching halt once you pass their property line. I use Silver's method and tell them calmly to go home. Getting off the bike would work well if you have a chaser determined to keep running. My mom had a rottweiler that would get out, if she ran after him or from him he would just run like the wind. It was all a game. If she stood still he got bored and came home.

Now cows in the road, that is a real danger in rural Texas!