Do you have a door between the warm part of the basement and the bulkhead?

I do. I keep bulbs in my bulkhead area and it works pretty well. I have foam boards and insulation stuffed across the top of the stairway. I keep the door closed most of the time (to keep the curious cat out), but when it gets really cold out (10-15 or less), I open the door a half-foot or so to keep it above freezing. I keep a thermometer in there to monitor things. My goal is 40 degrees.

Its good for forcing bulbs, but I have no idea about perennials. I sometimes keep those in my unheated garage with styrofoam peanuts insulation or next to the compost bin surrounded by bags of leaves.

I forgot to mention that the bulkhead is on the south side of the house. Do I have to worry that on sunny days it might get too warm in the bulkhead?

Thanks in advance for any advice!

I tried this once, and it didn't work at all.

My bulkhead's on the west side of the house; no insulation between the stairway and the bulkhead walls/doors. I put a lot of pots in there a few Octobers (or Novembers) ago, mainly tender perennials. Since I hadn't done it before, I went to check up on them a week or so later. The plants had all grown new, long, blanched-looking stems. The high heat during the day combined with complete darkness was NOT a good set of conditions for overwintering plants.

Maybe if the bulkhead were on the north side, or maybe if it had really good ventilation - or was made of clear plastic - it would work, but with a south-facing one, I wouldn't be very optimistic. Wendy's set up sounds like it might work, too, but I don't have an insulation barrier to keep the heat out.

My tender plants all go into the drafty detached garage these days, mainly to keep the pots from cracking. The occasional survivor, mainly curry plant and/or some salvias, is just a bonus.