M.B.
Hi K., being a somewhat big breasted woman myself, when I took up running, I had to get the support needed too!! I wear Moving Comfort Bras, the Helena ones http://www.movingcomfort.com/product/120385/350014/_/Hele... not in purple but you get the idea, that's the most supportive one I've found, and I've tried the Oprah Bra lol This one worked the best, my DD girls stay in place when I run with this. Go to sport chalet or something like that and try some out, jump around and stuff, you'll see. I've been looking online and I can see that Moving Comfort have new styles, you can look those up too, they look very nice and look like they have lots of support for the girls.
Good luck and good for you for starting to run, I started only 5 years ago and have run a marathon already, it's awesome!
M.