Lots of great suggestions.
But a couple more:
Try using Timtex or Peltex. You can sew through it and it is washable. Not as hard as the other suggestions, but does firm up the bottoms of bags.
You can also buy, or have cut, acrylic inserts for bags. The "Lazy Girl Designs Bag-E-Bottoms" are pre cut, with rounded corners in sizes that are designed for the Lazy Girl patterns. But one of the women in one of my Bag Lady Clubs has the local hardware store cut plexiglass to measure for her bags. Add a sleeve so that you can remove the acrylic, even be able to use the same acrylic piece in more than one bag. <G>
Have fun,
Pati, in Phx