How do I approach someone who rejected my facebook friend request?

Don't sweat it. Not everyone wants to be Facebook friends.

Yeah dreamcrush is right, had very same thing, but asked, they said oh I'm sorry I don't friend anyone any more, it's not you its everyone, turned out she just liked to see what was going on but not interact. Called being a - nosey bitch!

How do you now for sure that she rejected it?
I only ask because I've had instances when people had sent a friend request on FB but it went into my 'hidden' folder, due to my privacy settings. I didn't even know it was there until months later. (When I had first met my boyfriend, it was months later that he told me my settings wouldn't even [i]allow[/i] people to send requests...he had tried to send one and it didn't go through haha)

Perhaps she has the same type of settings?
I think you should ask her. :)

Nope. Don’t do that.

Or just accept they didn't accept you

Yes I would

obviously she likes the way things are, so no need to change it..

Accept her rejection. If you pursue her, you are a creep.