Inspiration: 3 Simple Bag Attachment Ideas
Now that you've identified what style of bike bag you wish to create, the next step is figuring out how to secure it to your bicycle.
Velcro or Hook & Loop System
Velcro can be the easiest solution, depending on sewing ability and fabric thickness. Velcro also comes in a variety of colors. You have the option of Velcro blending in with the bag, like the above photo. Double stitch, if possible, and sew ends to prevent fraying. For the more ambitious, how about backing the Velcro with pretty fabric?
Tip: Velcro is stronger than you think, but consider using it on bags intended  for hauling lightweight items. In this instance, I have used the bag while on a bike tour to hold valuables, easily removing it from the handlebar where it then becomes my purse.
While a bit more difficult to remove from a bicycle, leather straps and buckles provide a stronger alternative to Velcro. I think they add a certain amount of class, matching the leather handles in the above photo. Similarly, nylon webbing could replace leather belt. Or try cat or dog collars—a cheap find at a dollar store.
I sewed button holes and threaded straps. Another alternative: sew or rivet two horizontal rectangles of material on bag exterior, then feed through straps.
Tip:Â Cut leather longer than you may need. It's easy to trim it after, once you're sure of the length. Punch a few holes. Sometimes I attach it loosely to the handlebar, depending on the amount of things I'm carrying.
What I love about this solution is the quick connect and removal system. It has the added benefit of not snagging on clothing. Position the strap and hook & D-ring attachment correctly—appropriate to your bicycle—and you can avoid noisy jingling and/or marring of the frame or handlebar. This is also a bomb-proof solution, suitable for carrying heavy items.
And why not take this idea one step further? Next on my list is to reuse inner tubes in place of nylon webbing, using colorful stitching.
Tip:  Some purses already come with metal rings—a built-in place to attach hook & D-ring. You might search for these bags at a reuse store.
By using the above methods it's inexpensive and easy to up-cycle or recycle almost any bag or satchel into a carryall, exclusive to your bicycle.
I love others' ideas too. Or, if you need help, just ask.
Not into doing it yourself? No problem. Take a gander at my  bags for sale.
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*last photo, borrowed from PoCampo