I don't think you are ready to be in this relationship with her, I don't think you can handle the emotional honesty and maturity that she has.
You question whether or not someone with a swinger past can be honest and can be in a secure monogamous relationship. Yes, they can if they choose to be. I've been swinging off an on for (geez) 15 years. And there were times where I stopped completely because I was in a relationship that swinging was not a part of. If she cares about you then yes she can "turn it off". It sounds like it's been a while since swinging has been a part of her life anyway.
As others said, the fact that she told you at all says a lot for her. She could have not told you anything. Had you had this conversation with me when I was single, I would not have been able to give you a number and I would have honestly told you so.
There is a common bit of advice that goes something like this - "Don't ask a question if you aren't prepared for the answer". The old question of "how many partners have you had?" is not one that should be asked. If you are asking it, chances are you are not ready for the answer. If you are asking a question like that then you want the answer to be none or one or something "acceptable". Swinging is not something "acceptable" to most and it automatically has made you question her integrity. Then you came to the Swingers Board and asked if you should trust her? By questioning her integrity, you automatically question all of our integrity, so why do you even care what we think? You don't find swingers to be honest upright people to begin with.
At this point, you don't trust her. Move on, let her go find someone who doesn't question her integrity just because she has enjoyed others in her past.