I think right now you have to use the "log off" icon. This is not ideal because then you have to enter your username and password again the next time you launch the program. On my Android phone, there is a menu list instead that has an option to close the program, but you stay logged in so that next time you launch it you are already logged in. Hopefully an update to the application will include this. I suspect this update has to come from Pandora, not from BN.
After owning several android devices I can assure you that its not running in background. The way the android OS works is once a program goes into background or idles, its not using any of the CPU processor. This is consistant with all android devices. The OS is self managed..so just b/c you see the icon at the bottom of the screen doesn't mean its running. For reference simiply google or wiki Android OS. I currently own 5 android devices...some with custom roms etc..so I'm just trying to help some out who may not be use to how Android operates. Also...you don't have to logout..just leave it logged on..again its using little..to no CPU once its inactive and longer played.