Is a DGT Bluetooth Wireless e-Board stable enough to use regularly? I am considering purchasing a DGT Bluetooth Wireless E-Board for my school's chess club for exhibition games to be broadcast to a room without having everyone hovering over the board.

Are these boards sufficiently stable and reliable that, once configured, they can be used weekly without requiring any expert attention? I'm thinking both of the ability to detect what pieces have been moved and also the reliability of the Bluetooth connection.
Bluetooth supports distance of less than 30 feet, or 10 meters, and 802.11b is roughly up to 200 feet, though both distances depend on a number of factors; mention WiFi since it's possible that might be a better solution for your needs. Here's the DGT manual for "Connecting your Bluetooth board to your Computer", which might provide additional information of value to you. 

Also, it appears that the DGT boards do have problems, here's an example; note the pawn falls, and the screen does not report the pawn is not where it is suppose to be; note that the board is not the Bluetooth model, though in this case, I don't believe it matters; also, it's possible this is not a hardware issue, but related to the software used in the demo I've linked to just now.

Given that the board appears to be $1000+, it's unlikely you're going to find enough reviews to judge if it's a good fit for your needs. My suggestion would be to make sure that you're 100% sure it's possible to return it at near to no cost given the price of the board.

While not a review of the Bluetooth model, here's a review of a DGT board that appears to use the same technology, minus the Bluetooth.