If not using a mounting plate, routing a pocket into the underside of a wooden panel is a necessity. Fortunately, it doesn't need to be super pretty.
From that point, you can use whatever mounting method you feel comfortable with. Carriage bolts, L-brackets with short screws or 3M mounting tape, etc. The latter is good if you don't wish to have carriage bolt heads showing, but that is how they were on many panels, with the exception of those which used welded studs. Heck, you could even use plumbing strap to hold it in place, so long as the pocket isn't too sloppy.