Most do it yourself movers don't have access to a special canvas mattress bag or a large cardboard mattress box (by which to keep the mattress clean during moving). However, thin plastic mattress bags may be purchased from hardware stores which do provide rain and dust protection but their downside is that they allow the mattress to be very easily snagged or torn during the moving process.
So, whether you use a plastic mattress bag or not, still wrap a pad completely around just the bottom of the mattress if nothing else. The truck rental company will rent you all the pads you need for your move. So use a pad and just wrap packer's tape snugly around it in order to hold it securely around the bottom of the mattress while it's being moved. You won't need to tape the mattress itself, only the pad just as shown in the picture above.
Now, when you're moving mattresses, always keep the padded bottom down so that it can absorb any scrapes or dirt when the mattress must be briefly set down anywhere.
If for some reason a mattress must be flipped over, this kind of padding can be done on both ends to protect it. If a mattress has an unsightly stain on it, then do both ends and if necessary also pad the center to hide the stain.
Never set a mattress down anywhere that is wet even if you have a plastic cover on it because any little holes in it will allow water in..
Further instruction on how to best wrap, protect and secure other furnishings for DIY moving will be made available to you upon subscription to the site.