Mulch it deep, would be my advice. David, if it is a short enough pup, just pile mulch right up so it covers the top of the stem entirely. Those stems are full of water and if they freeze the water-filled cells burst, and whole thing collapses and dies back.
The point of mulching is to retain heat that is rising from the ground. The deeper the mulch, the more insulation you are providing. It also prevents freezing/thawing which can 'heave' up the ground around your plant. It gradually gets colder the longer the cold weather lasts of course but this is less destructive than freezing and thawing cycles. In spring, you can easily rake back the mulch to help the ground warm up faster.
Teresa, must admit I've never seen the point of wrapping a stem in burlap, unless you're worried about critters eating the stem. The stem itself doesn't generate any heat so wrapping it doesn't keep it warmer. You can wrap a human or an animal because they give off heat, and wrapping keeps it around the body. But a plant? - the burlap could even keep the stem too wet if it got a real deep soaking of rain at some point. Mulch insulates better because it is loose, with air pockets in it so it drains, and breathes a bit. Not sure about the bucket idea, unless you then cover the bucket with mulch to insulate it, too. If you're going to do that, forget the bucket. Unless you really want to keep the plant entirely dry as well. Hmm, not sure.
Now, if you wrap it with a string of holiday lights, that does generate heat. People here do that to keep their plants warmer on cold nights. But you can't mulch over the lights or it creates a fire hazard.
