I built my lathe bench using those wedged dovetail tenons. It's a good joint and you can tighten it up by tapping the wedge in harder.
You would attach the bottom rails at the bed and foot with mortices. I assume you'll use square legs, so there is plenty of room because you will have the side rails coming in closer to outside edge of the leg. Depends on the style of bed I suppose, but it's not unusual to have the bottom rails higher than the side rails to make access to the mattress easier for tucking in sheets.
"I don't practice what I preach because I'm not the kind of person I'm preaching to."