Nice Regal. I have a applicance repair manual from the 1970s that has part numbers for Regal cloth bags. For some reason they mention Regal while missing more common brands like Electro Hygiene. Anyway, they have them in the parts diagram for a Royal 601 and a Royal 801.
If you find the model number on your Regal, it would probable match the Royal model of the same number. I know all of my hand vacs are model 501s, regardless of the name on it (except for the Wards versions). They don't seem to change the number for different brand names. Oddly enough I've seen dozens of hand vac variations, and never an actual regal, or not one I can remember.