I had a hardtail chopper (Triumph) for a few years, never had a problem with insurance or police. The bike did have turn signals and a front brake and it wasn't stretched to a ridiculous degree, so that might have helped.
I suggest putting together some specs for your bobber and gather some pictures of bikes very similar to what you want to build. Then go talk to your insurance agent in person and discuss it. While choppers and bobbers aren't as popular as they used to be, there are still some out there, as well as lots of hotrod cars, so they must be insurable.