I have had it done, and it turned out weird- it was almost like the bras fit worse after being altered. I did some research and found that there are a few problems with getting bras altered. The first is that I was getting 30's altered, and I truly need a 24. (I would suspect the OP does, too, or at least a 26, since your waist size is 24" and your ribs probably aren't much bigger than that.) So, the problem is, there isn't really enough fabric to alter it small enough to truly fit.
Then the other problem is, if you have a small back size you need narrower underwires to fit properly. Basically, a B cup in a 30 back will have much narrower underwires and a deeper cup than a B cup in a 36 band, which would have wider wires/shallower cups. It makes sense if you think about it. So when you buy bigger and then alter, the wires are too wide compared to if you bought a bra designed for your size to begin with. And, altering the band stretches them out even more.
I have heard it can work for maybe one size, if you have no alternative. But you aren't going to end up with a good fit. And, btw, if you think a perfect fit isn't as important because you are smaller-chested, a properly fitting bra that's not padded gives a small-chested woman better shape than a padded push-up in the wrong size. (
http://stanikomania.blox.pl/2008/05/Wypchniecie-czy-upchniecie-czyli-push-up-na.html) (I found that on the blog
http://venusianglow.blogspot.com/ which I recommend for more information, as well as my own blog.
My suggestion is to try ordering online. I hear The Little Bra Company is coming out with C cups, and their bands run small, so why don't you try a 28C in that brand when it becomes available?