get 2 pieces of strong fabric put one inside the bottom in a u shape arrangement and one outside and sew using a stitch that looks like an overlocker one. lots of thread
you may need to quick unpick, undo the long side seam to ensure you don't shorten the bag!! while using sewing machine or over locker.
be easier to show than describe..
Edit you could use a pair of old jeans leg to line and reinforce, the bag