Many years ago we used to hold the bra straps to the shoulder seams with a couple of gold safety pins. The non-sharp side of the pins was sewn to the seam, so that you just had to slip the strap inside and fasten the pin. You could also get little bits of ribbon with press studs, to sew to the seams and fasten round the strap.
Those tapes they sew inside tops, presumably to keep the wide necks from slipping off coat hangers, can also be cut in half and tied round the straps.
All this needs doing when you get dressed, of course, and before you find yourself out in public, hitching up your neckline every two minutes.