Welcome to the forum. Did you buy King size singles ? or King size doubles? What sort of camper? What type of Bedding? The more info, the more answers when everyone comes back after the long weekend. By the way nice to meet you. Titch
King doubles are fairly rare. Check the exact size of the mattress then shop around. Sizes in different makes vary a bit. Kings are always very exxy relative to Queens (the most common double size) and if you buy an el cheepo make, you might find the sheets a bit tight and especially the fitted bottom one can pull out from under the mattress. I've seen ads for bespoke sheet makers who make them to fit weirdly-shaped caravan mattresses. They also make them sewn together at the foot for camping - some of the caravan magazines at the Library could provide some clues on who does this kind of sheet-making.
Pillow Talk is a good place to buy decent size sheets and if using a fitted bottom sheet make sure the wall is at least 30cm deep. In fact measure the depth of the wall of your mattress and then you will know what size to get.
I also find that Target have a very good range of generous size sheets and they often have percale sheets which IMO are the best. Yes a little more expensive, but better in the long run as they last and wear so much longer.
The worst day camping still beats the best day working