There are two things to consider here, ESD and wireless signal strength.
For ESD, it can be good to have a metal chassis surrounding the device going to ground to prevent discharges from humans reaching the device. The problem is the antenna's signal strength could be reduced from having a ground plane around it (if the metal chassis is around the whole bluetooth receiver, this would probably block the signal from the receiver).
You could get some software and analyze how the signal strength is affected by grounding vs ungrounding with a 2.4Ghz source in the place of the bluetooth receiver, but it would take the same or less time experimenting with different setups.
Try grounding vs ungrounding. It may be good to try a plastic chassis. SDR's are avalible that can be used as a crude tool for evaluating signal strength if there are not too many other sources around. There are also apps that can do this on a phone
If the enclosure works for the signal strength, with the enclosure tied to ground then I would use it to help protect against ESD