Step 1: What You'll Need
Thread (ideally one that has a nice contrast with the fabric).
Brown paper grocery bag (you can use any paper, but the grocery bag has some unique qualities that work better for this project.)
bottle to be wrapped.
Step 2: Making a Pattern - Step One
Align the bottom of the bottle at one edge, and mark the top (the point where you want the top of the bottle bag to be). You can make this longer than the bottle if you want.
Using one of the folds on the paper bag to guide you, draw a line from one end of the paper to the other. You can use a ruler, or you can use one of the folds from the paper bag as a guide to eyeball a reasonably straight line. (I drew my line using a fold as a guide.)
Step 3: Making the Pattern - Step Two
Align the bottle along that edge, and roll it up, like you would if you were wrapping the bottle with the paper.
When you've wrapped the paper all the way around the bottle, mark a spot at a point where there's about a 1/4" overlap. You don't have to be very exact. The polar fleece has a fair bit of stretch it in.
Unroll the paper.
Now fold that paper over, and use the edge to mark a straight line with a pencil where you marked the overlap. (Use the two perpendicular sides to help make sure that your line will be reasonably perpendicular to those sides.)
Step 4: Making the Pattern - Step Three
Slide your pencil along the side surface of the bottle, to help keep the circle that you're drawing centered around the bottle. This will also help keep the pencil perpendicular to the paper, so you won't try to trace the bottom where the bottle curves.
Go ahead and cut out the circle.
That should give you a square shape (for the tube part of the bag) and a round shape, for the bottom of the bag.
Step 5: Cutting the Fleece
Tip: Find which way the polar fleece stretches, and make sure that the long edge of your square piece is perpendicular to that. What you want is for the natural stretch of the fabric to be able to stretch around the bottle. (If you can't arrange your pattern pieces that way on your scrap piece of polar fleece, don't worry, this project will still turn out okay, but you may find the bag a little harder to slide over the bottle, that's all.)
If you want a fleece ribbon, you can also cut a narrow, skinny piece of the fleece. About an inch wide is skinny enough. Make sure that the direction the fabric stretches in is along the long length of this strip. After you cut it out, stretch the fabric as far as you can. Notice how the edges curl and it begins to look like a sort of rope. This will make a nice ribbon, and the curl will hide all of your raggedy cuts.
Step 6: Sew the Bag
Then, sew the round piece to one end of the tube. You may want to use pins to hold the pieces together. Or, you can take the time to hand sew this piece in with very rough stitches (that's called basting). Again, make sure you sew just at the edges of your fabric.
That's it. You're done with the construction part of this project.
I used a blanket stitch on my machine, but you can use a zig-zag stitch. (Most machines have a zig-zag stitch.) If you only have a straight stitch, that'll work, too. Just sew along the very edge of the two pieces of fabric. It's okay if you stray too deep into the fabric from the edges by accident; the polar fleece will still stretch around the bottle, and you can just trim the excess fabric away.
When you sew the long seam with a machine, the piece on the top will be stretched out a little longer, and at the end the two pieces won't match. Don't worry, you didn't measure or cut it wrong; the machine adds stretch to the top fabric as you sew. Just trim off the extra fabric so that the edge of the tube is all even again.
If you don't have a machine, you can even sew this by hand. Try to keep your stitches small. If your seams still end up looking kind of bad, you can just turn your bag inside out. This doesn't have to be terribly sturdy, since it's only a bag for a gift bottle.
Step 7: The Final Step
You can add a decorative stitch to the top edge of your bottle bag. I did a little zig-zag stitch around the top of one of my bags. You could also do a blanket stitch with some embroidery floss by hand. This can help hide a raggedy edge, if your cutting wasn't very steady.
Despite the lengthy description, this doesn't take very long to make. It took me about 40 minutes, but I had to stop and keep taking pictures. If you're a careful person, you only need to make the pattern once, and save it for re-using later.
If you'd rather not take the time to make your own bag, you can just cut to the chase (so to speak) and buy a pair already made at my shop at the Etsy website.