While we do not have pressboard under our beds (aluminum), we use an inflatable air mattress that sits on foam insulation sheets (4'x8') with the end cut off and placed in the "missing" spots to fill in the side spaces for a queen sized bed. On top of the air mattress, we use a foam topper. 

I bought  2  sheets of pink board foam insulation that they use on the side of house's and put that under our mattress .. Cut it out exact and it fits nice and snug. I use it for insulation from the cold/heat so you don't feel the cold wood board through the mattress. but i don't see why you couldn't use it for your purpose to keep the air mattress from getting splinters. other wise a real simple cheap solution would be to go to big box hardware store and buy a cargo blanket like $10.00  in hardware dept. lay that on pressboard before you place the air mattress down it will shield from splinters and also act as insulation