No, the spirochetes don't stay in the blood. They appear there as soon as you are infected, but their first order of business is to get out of the blood as a sort of self protection mechanism. They "understand" that they can't stay in the blood stream where they can be killed, so they migrate to the tissues, organs, bones of the body.
They move into the blood stream to reproduce every 4 - 6 weeks which is why we feel 'cycles' of symptoms in those time periods - not everyone, but many do.
Not only are the bacteria extremely small, but they are usually not in large quantities in the blood, so they have to be "cultured" many times just to have enough to see. Dark Field microscopy seems to have the ability to see them when other microscopes can't - but I would venture a guess that it has limited abilities as well.
The typical testing (ELISA & Western Blot) are not looking for the bacteria, but the body's response to the bacteria - antibodies. The problem with this is that these bacteria (& Bartonella as well) can inhibit (prevent) the immune system from 'seeing' the bacteria. So the testing is of limited value to many because the longer you go from getting infected until testing, the less chance the person has of getting a positive test result.
This is why even the CDC says on it's own Lyme page that:
"Lyme disease is diagnosed based on symptoms, physical findings (e.g., rash), and the possibility of exposure to infected ticks; laboratory testing is helpful if used correctly and performed with validated methods." (about
the only part they get right!!)
www.cdc.gov/lyme/