Technically you can put the songs on your BB, but they will not play. iTunes store music purchases with DRM will only play in iTunes or on iPods. There are several ways to remove DRM (Google it) including burning your music to CD's, and then importing the CD's as MP3's. I've even heard of a program that simulates the burning of a CD so you don't have to physically make the CD's.
You can also upgrade your purchases to iTunes+. This is a one shot deal for all your music, you can't pick and chose.
Apple is no longer selling music with DRM, so future purchases will not be an issue.