I did similar. But perhaps overdid it a bit......
I added 3/4" insulation to the entire under-bed storage area (the front curved wall, the sides, and the ceiling of the pass-through area. I then sealed all openings (two electrical outlets that really leaked air) with spray foam and then covered it all with plastic and luan (to protect the foam from damage). Under the bed platform, I added 1" foil faced foam (but no luan as I didn't want to add that weight to the lift arms) and then insulated where the platform sets on the frame with camper seal foam to reduce air infiltration there. Lastly, I put a piece of 4' wide Reflectix between the mattress and the platform (foam would have been better, but I didn't want the bed to get any higher).
At ~ zero outdoor temps, I noticed the bed was much more comfortable.
Steve