Ok, so it would be better to use re-usable storage containers, but sometimes a bag works better. First, determine how you will dry your bags. My husband made me this bag drying rack after he saw I had one on my xmas list that cost around $20. He spent a fraction of that cost and I have something prettier that he put forth the effort into making.
Then just save your bags and rinse with water (& soap if necessary). I generally wait until I have enough bags to fill up all the dowels so that I am not wasting time rinsing just one.
Now one could argue that you are wasting water with this and you might be. I'm not a scientist and don't figure out those impacts (just do online searches to see if anyone else has). But you are preventing yourself from consuming more plastic bags, so they are not ending up in the landfill and you are not adding to the production & shipping of more and you in turn do not have to spend another $3 to buy another box again.