Why do BBM messages show up in my e-mail inbox? Can this function be removed?

There's a setting for that in the options in BBM.
Yes, you can turn it off.

Thank you...but can you please describe exactly where in Options I can disable? If it's "Show Chats in Messages Applications," I've had that box unchecked, yet still receive the messages.

Yes, that's the setting.
Uncheck it.
It might not remove existing messages from your messages box, but will prevent new ones from appearing there.

Thanks, but still getting the messages. I'll take it in and have someone look at it.
Have a good day!

Make sure that after you uncheck that box you use the menu key and choose "save" if it's available. Then try a battery pull to reboot.