Change Bundle ID when "upgrading" to an organization from individual dev account?
The answer is somewhere in between actually.

If you setup a new organization account while keeping your individual dev account, you can transfer the app from one account to the other. In this process it is possible for you to choose a new bundle-ID for the app as an update of the app. 

However, the end-users devices will treat it as a "new app", which means that it will require them to update the app and the app will have "forgotten" any stored credentials in Keychain, and if you have any kind of sharing with other apps you have made, that group membership will be broken.