Bluetooth is not suitable for this. Buggy and high latency.
The latency shouldn't matter too much for broadcast/streaming.
Buggy is potentially a significant issue.
Bluetooth is fairly new, alarmingly complex, and evolving all the time.
Implementers also don't always do things the way the specifications intended.
I'm not convinced that makes it unsuitable for this use.
I'm not sure there's an alternative that would be suitable without dedicated gear.
Something on WiFi with a App might be more robust.