I think the most secure way is to sew it down with a sewing machine, but that's not particularly elegant. Elegant would be something like grafting the things on by picking up some stitches on the body of the bag and then grafting those with the straps, but I'd recommend sewing the ends down in that case and weaving for good measure.
OTN: Eyelet Chemise in Handmaiden Sea Silk (colorway: Midnight). Still. And a purple Donegal Tweed set of fingerless mitts, to try out my new Hiya Hiya interchangeable needles.
Latest FO: A shrug for an Anthropologie swap in beautiful Casbah sock yarn, in Cedar, a dark green semi-solid, my own pattern. Also a quick Noro Silk Garden neckwarmer for my friend Aideen, in a vine lace pattern.
My knitting blog, Another Long Yarn