You can usually get double strength garbage bags from large supermarkets (the heavy orange ones work well) and you will need at least two if you plan on properly sealing a backpack inside (and a third if you plan on crossing any rivers deeper than your waist).
Another use for plastic bags is insulation. If you have something that doesn't need moving (or if you dont mind a crinkling sound when it does) then you can stuff it full of plastic bags to keep whatever's inside warm. All the little air pockets amongst the bags will trap heat for a surprisingly long time.
Some easily obtainable more medieval looking alternative ways to carry things are:
- calico bags
- pouches (eg a sewing pouch, games pouch)
- wooden boxes
- tied up in a piece of cloth or garment of clothing
- hessian sacks
- old leather school satchels
Most of these do not have the waterproof attributes of plastic bags, but can be lined with plastic bags if inclement weather is likely. Medieval solutions to waterproof carrying included canvas sacks, including tarred canvas bags for sailors, expensive well crafted boxes that fitted without leaks, and well built barrels (if it can hold water in, then it can also keep it out), and use of waterproof leathers. Multiple layers of fabric could also be used, such that the outside layer might get wet, but the inside ones would not. However there is no doubt that plastic bags have superior waterproofing to medieval materials - they require less maintenance and are very cheap for a start.