I believe something like this was featured on that one invention-competition show on TV...
AND I saw a girl when I was in Vegas that had one of these and I ALWAYS kick myself for not asking her where she got it or how she made it or w/e.
Anyway...when I do anything backless I do one of two things ---
Walmart has these stick on bras, where it looks like a regular strapless bra in the front, and on the sides it has stickers -- and then I also pin a clear halter strap into the cups for extra support. http://www.walmart.com/catalog/product.do?product_id=4196156
OR, they make the bras with the clear strap that goes around the back...I know, it's not totally strapless and you can see it, but on first glance it does look like your back is bare, and beggars can't be choosers
H&M sells them for $14 or something cheap like that. (Rainbow also sells them for 2 for $10, but I imagine the quality will be MUCH less...if you want to go higher up in quality, Victoria's Secret sells them for something crazy like $50).
Another idea I've been toying around with is replacing the back of a front-clasp bra with a clear shoulder strap, so it's the same idea of the "clear strap around the back" bra but the strap is much thinner...