My suggestion would be to contact the school directly and find out what they really want.
The suggestion of fabric ties is good ... though the staff, may not want to be bothered with tying those up each day. Thus might prefer the elastic. And is the elastic to cover the cot over after used and until the next day? Someone said it is removed from the cots each day ... yet at one school, I know they leave the child's belongings on the cot, and then stack all the cots together. So if this were the case, the elastic may be to help keep all his belongings together.
I know I may be throwing a monkey-wrench into your thoughts ... though for me, I'd sooner spend some extra time in checking it out, than to do all the work, and discover it is not acceptable!
Totally cute fabric .. will be fun to make and fun for him to enjoy!!