What benefit would explaining BDSM to your family bring to you? My parents and I are close, though I can't really see how my sharing my intimate activities with them would be a real bonding conversation.

On the other hand, if I were bisexual and were in a same sex relationship, it WOULD be important for me to be honest about that relationship and to be proud of the person I was with and committed to. That I wouldn't keep private.

It just comes down to what you want - if what you're after is simply to alleviate the worry and problems that your lack of openness seems to be causing, there are ways to be open yet still discreet. Tell them you're not seeing anyone, tell them you're only interested in casual dating, whatever. Start small.