Bunk beds do not need special mattresses.
When you buy a mattress you can buy a standard regular mattress for the bunk bed.
Most bunk beds use a standard twin mattress especially for the top bunk and some bunk beds may have a bigger mattress at the bottom.
But then again some bunk beds have the same size of mattress for both the top and bottom bunk.
My kids bunk bed has both the twin mattresses on the top and bottom bunk but I've seen some bunk beds that use a full size mattress on the bottom and a twin mattress on the top.
It's recommended that you put a piece of plywood underneath the mattress for extra support but it's not a requirement.