MIKE R Although I use a different style bivy shelter (mine opens from the side and not the top) I do use an air mattress and have never had an issue with it moving around. These shelters are usually only big enough for one person with the possibility of storing gear at the "head" and "foot" so your air mat can't really go anywhere.
Michael D. G Thanks MIKE R.,for the input.And this is what's so appealing about this particular bivy is the length,head room for stowing gear.OR bivys all have mattress straps so I thought I would at least ask...HikerMiker