I have a few bed sheets that I brought from China when I came to Australia. They're quite old fashioned but they're pure cotton and very comfortable. In China we never used mattress covers. In fact we only started using mattresses in the last couple of decades. I still remember when in Uni we only had underlays (thicker than the ones I found here in Australia) on bed, and we wrapped the bed sheets on the underlays. It was very comfortable. Actually I hate the mattresses we have now in our home as I have back pain and the mattresses are soft (I already got the hardest one in the shop) and my back pain can only get worse.
Anyway, since now we have a few more single beds in the house, and we don't have any single mattress covers, and the bedsheets are a pain to wrap around the mattresses, I decided to pull out these old bed sheets that we don't normally use and put them into good use.
I measured the single mattresses (they're of different thickness!) and measured the bed sheets. This pinky/yellowy bed sheet is fortunately larger than what I need so I just cut off some and sewed the four corners and threaded in some elastic and voila, a beautiful mattress cover!
Then when I came to this bluey one, it's shorter than what I need. Lucky it's a lot wider so I cut off the sides and used one of the strips I cut off to connect the top and bottom. So still a beautiful mattress cover!