Do you have to have a special type of mattress for bunk beds?

It depends on the bunk beds. Many have mattress thickness (height) restrictions so that the surface of the mattress is not so thick that the top bunk is unsafe (the surface of the mattress, if too high, will come too close to the top of the guardrail.)

If there is a height restriction, and your daughter will be sleeping on the bottom bunk, you might want to consider purchasing an innerspring mattress for the bottom bunk where she will sleep, and a foam bunkie mattress for the top bunk where there will only be a person sleeping occasionally.

If she is sleeping on the top bunk (make sure she's at least 6 years old... older is better for the top bunk) then you'll need to observe height restrictions for her safety or have a custom furniture builder make adjustments to the height of the guardrail.

Also, you need to find out if the style of bunkbeds she's purchasing requires the use of a "bunkie board" which is a platform of sorts that stabilizes the surface under the mattress since there is no box spring used under the mattress in a bunk bed. Some beds have a platform already (you can just top these with a mattress) but some have rails that go across and you may need a bunkie board.