This summary is for all the people who do not want to read the whole thing. Locate the folder /steamapps/Shadowrun Returns/Shadowrun_Data/Mono. Delete it. Use Steam to verify game cache and it will pull all the files again.

If bluetooth audio is generally correctly configured and you know this somehow then something to try out is to set your bluetooth headset as the default sink for pulse audio.

You first identify the device you want to set as the default sink. To do this type:

pacmd list-sinks \| grep …