What is a typical duty cycle for Bluetooth headsets playing music?
This is the RX bandwidth very rough estimate:
We have to assume few assumptions:

AAC bitrate is 128Kbps
Bluetooth 5 is used.

Bluetooth 5 datarate can be anywhere from 250Kbps to 50Mbps. Lets pick a reasonable 2Mbps, that gives a rough duty cycle of 12.5%. Actual duty cycle will be higher (protocol overhead, network overhead).
TX Bandwidth will be lower than that, it is mainly control and network management frames. Usual keep alive period for a BT device is 1 sec, but it is highly dependent on the device and power saving settings.