I, too, don't have any magic solution...all I can do is share your pain! I'm also naturally busty, and going without a bra in public is not an option. Like many of the other posters, my bra is the last thing on before I leave the house, and the first thing off when I get home.
The only suggestion I can make (and at best it will be only marginally helpful) is to make sure you wear the proper size bra. So many women wear too big of a band size, and too small of a cup size, and that puts too much of the "load" on the straps.
The center of the bra should fit right against the breastbone, and the majority of women will find that (I repeat) they need to go up one (or even several) cup sizes and down in band size.
So far, that's all I've got for help--I hope someone else can post a better answer. Good luck!