Have a pit bull mix on my regular route. Going, I can get by him before he realizes I am there. On the return trip he is waiting for me. Up until today I would let him start towards me then crank like crazy and out run him. Today I was battling a very stiff headwind on the return trip. That coupled with being tired from not sleeping good and the road in that area is a solid series of patches, I stopped the bike, got off and pushed the bike. And while he barked the entire time, he stayed in his yard. So it looks like I have found an answer to that dilema.
I have a CCWP, but would hesitate to shoot a dog. For one thing, I like dogs and I know how attached people can be to their dogs. And you run a real risk of the dog owner shooting you. I know that around these parts, people that like to keep mean dogs are generally aggressive people. Pepper spray is probably the answer, although you will have to be careful and not spray yourself or a riding partner. I had a local police officer tell me that they did not like to use pepper spray because he said eventually you WILL get some on yourself.
BTW, all the other dogs on my route like to run with me.