The best way to transfer your BBM to a new phone is by moving the application to your SD card. Every android phone has this feature and you can do this from the settings / applications section. Select BBM and choose move to SD card.
By moving your app to the SD card you're also moving its root folder. Once moved out of your handset, place the SD card into your new phone, re-install a new session of BBM, sign-in and your files will be there ready for you to enjoy.
