Another thing that I have done when I had egg toppers, and sheets that were not deep enough to hang onto the topper and the mattress was to use two fitted sheets -- one on the mattress underneath, and one only on the topper. This way I was able to use the sheets I already had on hand; it wasn't ideal, but it served the purpose.
You can buy the elastic straps that clip to sheets on the under corners to hold them tight, or make your own out of old overalls buckles, or alligator clips, and elastic. This way you can probably use sheets you already have! I have found that specialty sized sheets usually cost way too much.
I doubt if any regular size sheets will fit your bed well. This site has sheets for camper beds, they claim they will never slip or come off unless you take them off. You can look to see what sizes are available. They also make custom camper bed sheets.
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