Although the bacteria that cause Lyme disease have been found in body fluids, there is no hard evidence of person-to-person transmission. The bacteria have to be injected into the blood stream, which is where the tick comes in. The tick also injects immunosuppressive chemicals which can prevent the immune system from recognising and dealing with the infection. So, it would be very difficult to infect another person, although that doesn’t mean it could not happen.
Don’t forget that you breathe in, and have contact with, a whole host of viruses and bacteria every day, but you do not catch disease from all of them. There is a highly evolved relationship between the tick, the bacteria and the host – human or mouse etc. The tick injects the bacteria into the blood stream together with other compounds which aid survival of the bacteria.