Do the bumpers have to be attached to both the top and bottom of the frame
No, there is no rule that requires that. A lot of teams make brackets like these ones from Andymark. Attach the bottom side to your frame, usually on the top so it is easy to get on and off, and then attach your bumper through the top hole. Usually two of these brackets per bumper/side is all you need.
If you need any more help, just send me a PM and I may be able to dig up some pictures!