I make bags and purses using quilter's cotton. I use pellon sf101 to interface both the exterior fabric and the lining.
works well, providing strength and stability in bags and purses.

I would use the canvas as the base to sew the fashion fabric to, sort of like MSQC does a QAG. That way you get durability, strength, and beautiful fabrics. Win, win.

I use "ByAnnie Soft And Stable" and I love it. I tried it for the first time after making many bags without it, and now won't make a bag without it. It's strong yet soft.

You could use two layers of fabric quilted with batting or fusible fleece between them. Determine the size of fabric you need. Fuse fusible fleece to one side of one piece, layer another piece of fabric on top of the fleece and stitch together in a grid pattern or just straight lines or do a free motion quilting motif on it (great way to practice free motion quilting btw). Then assemble your bag with straps as desired. Have you seen the pre-quilted fabric sold in stores? It is usually more expensive than regular cotton fabric and not in the colors you are looking for, but this is the same principle.
Can I ask what you plan to carry in your bag that you are worried about the fabric ripping? I have carried books, groceries, etc in the bags I have made with this method and not had a problem.

I have made this bag and it has held up fine. I made sure I re-inforced the stitching on the handles. The webbing comes in so many colors and I could match my handles (JoAnn's) to the webbing!

When making bags and purses, using the proper interfacing for your project is an important part of the construction process and can make or break the design of your bag or purse. Interfacing adds support and structure to the style of the bag, and also strengthens and stabilizes the fabric and prevents it from distorting and stretching out of shape.
There are lots of different types of interfacing available however my personal preference for bags and purses is to use fusible interfacing. Fusible interfacing is easy to use and comes in a wide variety of thicknesses and types. Depending on the type of interfacing, it will have a rough texture or shiny surface on the fusible side, and this is the side that fuses to the fabric. Most fusible interfacings are nonwoven which means they don’t have a grain and you can use them in any direction.

I purchase my fusible interfacing from "Creative Cloth.com" online, there are many different types, you will see that on their website.

My brick collection! ;)

I don't have a particular use for it, but I want it to be strong enough for things like books. In the past I've made it with a single layer of canvas, but a single layer of thinner cotton isn't going to do it. Something like you have here with the fleece would be better.

There are so many good ideas here that I keep changing my mind about how I'm going to do it. I'm leaning towards something like you describe here, but since I already have regular fusible interfacing, I'll probably use that instead of going out and buying the fusible fleece.

Thanks everyone for all the posts. I've learned a few things that I want to try out, and since bags go together pretty quickly and are so useful, I'll probably have a chance to even if I don't for this bag (unlike quilts where I'll never get to half the things that sound like fun).

I'd test out some different types of interfacing. Many people like to foam.

I just got my mini bow tucks pattern and am dismayed at the lack of step by step pictures. This will be the equivalent of a mystery project for me... wish me luck. Yours is very pretty. I really like your idea with the random stitches placement. My first one will be the test before I cut into my pretty fabric.

Pellon makes a foam that you use for bags that gives it structure without the weight. You might look the next time you are in the fabric store at the available new products by pellon. The sheet that comes with it has all the instructions on it. I bought a lot of it but haven't tried it as yet.
I usually cut my main outside fabric pieces large and quilt them with the 80/20 batting on the back before cutting them out to size. I consider the use of the bag and where the structure will have the stress and quilt accordingly to stabilize it. I sometimes only quilt to the stitching line so I can cut away the batting in the seams to reduce the bulk so I get sharp edges.
I hope this helps you. I have made many bags and each one needs it's own thought and process before making it.

The picture in my avatar is the front detail of a bag I donated to the diabetes auction in memory of my friend kitty.