Step 1: Determine how big a piece of fabric you'll need
First, measure the box, both around the sides (S), and around from top to bottom (T). Write those measurements down. The measurements don't have to be really precise. You can round up to the next inch, and it won't affect much. You're going to need some ease anyway.
Now for the math. The fabric will wrap around the bottom, and you'll be making two side seams.
First the width. Now since you need two side seams (to have ribbons to pull to both sides, you'll take the S measurement and cut it in half (S/2), then add seams plus a little ease, so that you can get the box into the bag. I tend to be generous, so (S/2) + 2" for the width.
Next the length. Start with the T measurement. You'll also need about two times the size of what ever ribbon you'll be using as ties. I used 1/4" ribbon I had sitting around, but I don't like to go less than 1" on the drawstring, for looks and usability, so I added 2" on both edges (+2" x 2). Plus twice a nice ruffle on the top. The bigger the box, the bigger the ruffle needs to be to look good. I thought a 4" ruffle would look good (+4" x 2) And, you'll need that ease as well, plus some to finish the edge...about 2" again. So T + (2 x ribbon width)+(2 x ruffle height)+2"(ease+top edge finish).
As you can barely make out in the picture above, my box was 31" around (S) by 23" top to bottom (T). So my formula was (31" / 2) + 2" = 17.5" for the width, and 23" + (2 x 1") + (2 x 4") + 2" = 23.5" for the length. So I needed a piece of fabric that was 17.5" x 23.5".
To check, you can lay out the fabric, and fold the fabric around it, to make sure you haven't missed any thing. I found a piece that was a bit bigger in both directions, and just used that.