I use 2 layers of plastic canvas - have been very lucky to find it at garage sales or thrift store. I did use cardboard one time, thankfully it was my purse! I accidetally knocked over a cup of soda on the car seat where the purse was sitting - destroyed the cardboard and had to make a new bottom for my purse.
Have also recycled some plexiglas for purse bottoms - I did sand the edges and slightly round the corners so they would not wear through the fabric covering. No problem so far and one of the purses I've used for about a year now.