I have a heavy canvas duffel that I use for my range bag. It has zipper compartments on both ends and one on one side. I put all my .40 and .22 rounds in it and just grab it when I go to the range. I must have 500 rounds of .40 and 1000 or so .22 in there, in addition to my Glock and Ruger pistols, hearing protection, assorted screwdrivers, oil, rags, etc. It works fine.
Make sure that the straps go all the way around the bag instead of just being sewn to the top.