A blow up bed would be a nightmare! The clean up after a bed birth is easy. When you are in early labour you (or your birth partner) strip the bed put your favourite clean fitted sheet on. Then cover this sheet (and so the mattress) with 2 shower curtains. Place another old fitted sheet over the top and put your favourite clean duvet cover on - the whole duvet will be moved when you are in labour - in another room or just out of the way in your bedroom. Have clean pillow slips with it just in case.
Your MWs will put the same inconti pads on your bed as they would on their own hospital beds - they soak up A LOT! If you want to be doubly sure you can put a towel down too.
Give birth....
While you are getting cleaned up your MWs/birth partner/s simply bin the inconti pads (mws take all this kind of stuff away with them) and chucks the top sheet (and towel if used) in the wash, removes the shower curtains (to reveal cripsy fav sheet beneath) replaces the duvet and pillows on the bed (they dont usually need new pillow slips but they are to hand if you want everything super fresh and yummy to get into!) and voila! You get in to crispy clean bedding before you can say 'crack open the champers love!'.
Typed out that sounds long but it's 5 mins prep and 5 mins to sort after.