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The key is to use a walking foot or dual feed on your machine - it grips both layers evenly and stops the bias tape from bunching or shifting on those curves. Pre-fold and press your bias tape before attaching it, and go slowly around the curves, letting the machine do the work rather than forcing the fabric through. Some people swear by pinning like crazy or using spray starch for extra grip, but honestly a walking foot makes the biggest difference if your machine has one.
Once you've got that walking foot sorted, slowing your machine speed way down on the curves is honestly what makes the difference - you need time to guide the tape smoothly without it puckering, especially on tight turns like necklines or armholes.
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