I have an eBags Kayla Town Square tote that has a bottom with 2 adjustable straps (which can be zipped up and hidden away) made specifically to accommodate a yoga mat....or any other large object that can be rolled/folded/squished, such as a snow parka.
http://http://www.ebags.com/product/ebags/kalya-town-square/57682?productid=10019411 which also comes in black and a lighter red called Chili, but both of those colors appear to be temporarily sold out...