Will my acrylic painting be safe?

I have just bought a canvas bag to use as a purse. I was hoping to make it my very own and paint an original design on the fabric. I have acrylic paint that I can use but will my artwork be able to withstand the wear tear of being on fabric instead of a stretched or solid canvas? Should I use a different medium or buy a "paint saving" substance? Any help will be ENORMOUSLY appreciated. Thank you.