Our friends at Topeak make some really good bike bags - they are expensive, but they work really well. I've given you a link to the bag I own - it can hold your day's goodies and clothes for a ride-to-work day, or some groceries for a chores day, or plenty of picnic for a day off.
To use a Topeak bag, you need a special carrier on your bike. But once you have the special carrier, you can slide ANY matching bag onto it.
So, what happened was, I managed to tear my older Topeak bag (it was a bit less cool than the one in the link). I repaired for a bit with duct tape, but it was pretty torn. I replaced it with the cool one I have now. I finally decided the torn one had to be retired. But first, I took it apart (as you do). And discovered that the whole mechanism that clips onto the special carrier was just fine!
So, I bought a pretty canvas bag at a local op shop, and here is my new bike bag!
38 minutes ago