When you "dismount" your bike, you don't necessarily have to get completely off the bike. Just getting off the saddle and putting your feet on the ground is often enough. If you do have to put the bike between you and the dog, swinging your leg over the bike is a pretty quick move, especially when you are already standing on the ground.
By the way, you can explain dogs to people, their relationship to humans, and the fact that many dogs can run 30 to 35mph until you are blue in the face but it won't help. The fear of dogs is just something you can't talk people out of.