Basha-
Helen's idea of *tubes* works good ((been there / done that ;-D ))
- and -
there's keeping the side strap stretched out while stitching your fabric to it - use whatever is handy that has the same measurment as your ribcage - I've heard metal buckets work great!! ((been there / done that, too - except I have a dress dummy named "Mabel" ;-D ))

I do indeed sew the duck cloth directly onto the sides of the bra. For me, that's the "super quick easy way" to do it. So, when I'm in panic mode over needing a costume ASAP, I'll do that and sew it with a machine and wind up with a nice, strong strap. I do this, too, because usually I put tons of deocrations on the bra and even sometimes on the sides so I want a nice strong band to support the cups. There are TONS of other ways to make the sides - the tube is a great idea! - and I'll try to post some photos soon of other ways to do it.

One idea that might work for you: sew using the ZIGZAG setting on your machine. If you use this, or a smilar stretchy-stich, your bra will stil stretch as long as the material you use has give. It works wonderfully with crushed velvet! If you skip the duck cloth, you can cover with crushed velvet and stich over in zigzag and have plenty of stretchy breathing room.

A note on elasticity: remember, most mass-produced cabaret bedlahs never have stretchey sides (or at least the 15+ that I have don't! if they're out there I'd love to find them!) so I guess I'm just used to wearing those and as such make my bras in much the same way when I'm building a costume. :)