I'm confident that you're parents might trust you, it's you're bf they don't trust. I'm a male, if a girl asks me to spend the night, I'm assuming it's for sex. Youre sending the wrong message. Only way I see is have him over for dinner. And bring it up, try not to make it too awkward, aim for the end of dinner, so everyone is finished eating and it's a quick bye to avoid the awkwardness.
How old are you? Firstly, until I got college age, there is no way I would seriously ask that of my mother. Unneeded stress!!! But if your that determined for whatever reason approach it honestly, don't argue if the answer is no, and most def sleep in separate rooms!! And, don't give parents a reason not to trust you!!! Gah. I have to remind my younger sister of this every day. Believe me. Life is a lot easier when your parents can trust you. Unless they are just crazy. 8-/