It's done, and turned out fairly well, although not absolutely fantastic. At the last minute, I decided to use a third fabric for the bias trim: Amy Butler martini bubbles in yellow/pink. It picks up the little bits of pink in the exterior fabric, and the bits of yellow in the lining very nicely, so I'm happy with that decision.
Sewing the bias binding in place by machine in one pass was adequate, but not great. Partly I think because I was working with more and thicker layers. It looks okay, but I wasn't sure I'd be thrilled with the exposed stitching, and yeah, I'm not loving it. On the other hand, I don't dislike it enough to rip it all out and do over the other way (see #2, below).
What I'll do differently next time (if there is one):
1) Make the strap a bit longer; I'm on the tall side, wish it hung just an inch or two lower
2) Use a quilt-style binding: i.e., fold bias tape WST, align raw edge on top, stitch in place by machine, then turn fold to inside and slip-stitch by hand to finish.
I'm sticking with my rule that I have to finish one UFO before I can start a new project. Next up: the "muslin" for Simplicity 2957 is close to done, and looking pretty good at this stage. Whether I will like it enough to wear enough to be worth making from nicer fabric remains to be seen. Which is the whole point of making it from quilt-fabric stash first.
When I finish that I want to make something with sleeves (cooler weather is here, at least on overcast days) from some of the cotton lawn in my stash. I set some (non-sewing) tasks aside, though, to get the tote done, so don't know that I'll get back to sewing for a few days.