My siblings and I kept mattresses on the floor in our teens and twenties. We didn’t have problems with bugs or mold, and we live in New Jersey with hot, humid summers and the house did not have air conditioning. I found it quite comfortable and more supportive of my back.
As @johnpowell said it might promote the growth of mold but you can just lift the mattress up and lean against the wall in the morning after you wake up. This would be a solution to prevent molds. If you turn your mattress daily and change and launder your bed linen then there won’t be any bug issues too. In case there is mice or cockroaches then you need to be careful.