Turn the bag inside out and line up the lining with the bag corner edges and machine stitch the lining to the seam allowance of the bags corners. I am assuming it is a squared bag bottom.
You could also sew buttons on all 4 corners on the bag outside for the purse to sit on and it will allow you to hand stitch them from the inside to anchor the lining as well. Adding feet to the bottom of a bag helps to keep the bottom clean.