Here is a short english description how to configure the iRig Bluetooth with SongBook+.
(The image below is a bit old and in german but the english text in the description here matches to the image. The MIDI settings are located inside of SongBook+ app and not as shown in the image in the Settings app.)
The blueboard app must be started and configured in ControlChange mode.
Configure it to send 4 different ControlChanges for the 4 buttons, e.g. ControlChange 10,11,12,13.
Then open the MIDI footpedal settings of SongBook+ and enable "Use MIDI foot pedal" and select the same MIDI channel that is configired in the blueboard app.
Then configure 8 configurable ControlChanges in the MIDI footpedal settings of SongBook+ as follows:
Set the first configurable controller entry to "If controller 10 changes to 0 execute this action" with the desired action,
the next to "If controller 10 changes to 127 execute this action" with the same desired action.
Do the same for controller 11, 12, 13. Always two entries with same controller, but once with value 0 and once with value 127.
(The Blueboard alternatieley sends value 0 and 127 for the same button).