it would be interesting to know what bluetooth device is installed on your system.
Sometimes, certain bluetooth manufacturers don't work very well with certain devices. Often, changing the bluetooth driver to Microsoft stack, or changing it from Microsoft to the manufacturer's latest driver version, may resolve the issue.
Find out your installed bluetooth device and try googling for its drivers, if you haven't got the latest ones.
Also, you might check your laptop manufacturers website. They have the bluetooth drivers pertaining to the specific model in question, which are modified to meet the laptop's specific device configuratiion.
Sorry to be a bit vague here, but other than that, I don't really know what to suggest.
Also, is automatic detection of bluetooth displays turned on or off in JAWS settings?