Look at sample rate, typically a lot of Bluetooth devices are single sample rate, either 48khz or 44.1khz.
In your case an audio file plays OK - is it a 44.1khz file?
Video files normally have a 48khz sample rate for the audio tracks so if they don't play it may be that your Bluetooth device is a 44.1khz only device.
To check, open the Windows sound settings and check the supported sample rates in the 'Advanced' tab of the device properties.
If it is a single sample rate device then just set MC DSP 'Output Format' to the same output sample rate for all possible input sample rates.
However, you also say that DirectSound isn't working correctly either, in that case the Windows mixer usually handles the sample rate conversion so you may have another issue entirely.
If you still can't get it to work perhaps post a few more details of your Windows, MC settings and the Bluetooth device.
Good luck.