I assume you're using GMail. The reason for this issue is that GMail's inbox and sent box are only separated by labels (despite how it looks online) and therefore BIS sees sent messages as in the same folder as your inbox and retreives them.
It's very simple to fix.
Go into your BIS account and beside your GMail address you'll see little icons- hit the Filter one, and create a filter that doesn't retrieve any emails with your gmail address in the "From" section.
Set that up and the problem goes away!
You will still receive emails you send yourself on your BB for some reason though...which is fine with me!