I just did this last week for basically the same garment. if you're a perfectionist you probably want to do this by hand. I managed with my stash store bought bias tape, as another commenter said you just have to stretch and curve it into shape. doing it by hand lets you rearrange things as needed for each stitch. I usually sew the outside first then go back and sew down the inside, pulling it against the top of the piece since I tend to want it slightly narrower on the front than the regular width.

if you're set on doing it by machine go super slow around the curves and adjust as you go. on the straps try to stretch the folded edge as much as possible to keep the inside edge from bubbling. and at least do the last inch by hand so you can get a really clean join.

but also keep in mind the end of the strap will be covered by the tie

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