I can definitively say the GW will control the BB. The GW won’t talk directly to the BB so my iPhone is the intermediary.
I got the GW for 1/2 price thanks to FLR and finally got it to control the BB. I’m using the Yamaha MD-BT01 wireless (BT LE) MIDI interface with the BB (no batteries needed for the MD-BT01 unlike the PUC which requires batteries). I programmed the GW using the programming app available from the Lividinstrument to send the midi commands that work on the BB. The GW programming app uses a scale of 0-127 (vice 1-128) so tune the numbers accordingly. I had to set the buttons to toggle to get them to work correctly.
For apps - Apple iOS doesn’t seem to recognize midi BT devices on its own. I used the Yamaha Digital Piano Controller to establish my connections to the GW and the BB.
http://usa.yamaha.com/products/musical-instruments/keyboards/apps/dp_controller/?mode=model
Another BB user (Mans Martensson) reports success using the PUC app.
https://itunes.apple.com/us/app/puc-connect/id821789942?mt=8
Yamaha also has a utility app specifically for the MD-BT01 that might work but I haven’t tried it yet.
http://usa.yamaha.com/products/musical-instruments/keyboards/apps/md-bt01_ud-bt01_utility/?mode=model
To route the midi commands from the GW to the BB inside the iPhone, I used an app called MIDIBridge ($9).
https://itunes.apple.com/us/app/midibridge/id449160859?mt=8
Mans said he used AUM Mixer successfully for routing - it appears to do that and a whole lot more but it’s $19.
https://itunes.apple.com/us/app/aum-audio-mixer/id1055636344?mt=8
So far, the GW does basic song commands - start, fill, transition, muted pause, and outro. I haven’t gotten any of the tap tempo controls to work to date on either the GW or the midipad app on my iPhone so that’s still a work in progress. I also haven’t tried it live to be able to say whether or not the GW is better than the foot pedals.
I’m using a 6s plus iPhone running the latest version of iOS (9.3.2 I think).