You used to be able to buy little ribbons with press studs that you sewed into the shoulders of dresses and blouses to secure bra straps with, but I haven't seen any for years!
Some of the problem is that the straps are made of slippy material, sometimes it is a matter of adjusting them correctly, which means putting on bra, taking it off, adjusting straps and putting it back on again a number of times until you get it right.
Has anyone tried tacking a thin piece of foam rubber to the back of a bra strap? It might help.
I have stopped sandal straps from slipping, or even worse digging in to my foot by putting a piece of the sticky-backed foam insulating tape for windows and doors on the inside of the offending strap. It does work.