Wait- you want opposite. BM video, but "system" audio.
Make sure it' set to Mac speakers in OSX preferences (also look at Audio Midi Setup).
In Premiere you have 2 places to setup audio:
Audio Hardware and Playaback tab. Look at both and make sure it's not set to BM anywhere there. There are quite few settings which may affect it.
Other work around (for non critical monitoring) is to create "Multi-Output Device" in Audio Midi Setup:
1. Open Audio Midi Setup
2. Click on the + at the bottom and choose "Create Multi-Output Device":
In my case it's Mac speakers and DragonFly DAC
For BM make sure you set sampling to 48KHz!3. Open Premiere and in Audio Hardware choose this as default device for playback:
and Map Output to Adobe Desktop Audio
4. In Playback setting make sure that Audio Device is set to "Adobe Audio Device":
this should give you audio from both- BM card (so your TV) and Mac speakers/headphones.
I tried it with my DragonFly and it worked fine. There may be some issue as BM is multichannel device, but it should work for stereo. If it works you don't have to keep switching anything- you always have output on both devices (just mute not needed one for given time).