Baby mattress blues...

My DD seems to hate her bassinet mattress. I have a tempurpedic bed (memory foam), and I can lay her in bed with me to sleep for hours. Add soon as I put her in her bassinet, she either wakes immediately or we get a half hour at best. She will happily sleep in the bassinet on her pack and play because it is cushiony and suspended. I'm at a loss for what to do. They say you shouldn't Co sleep which it freaks me out anyways, and I wind up staring at her all night. I'm afraid the same thing will happen when we transition to her crib as it is also a very firm mattress. Any recommendations on softer beds?