How secure is a bluetooth keyboard against password sniffing?
While Bluetooth has its benefits, it is susceptible to denial of service attacks, eavesdropping, man-in-the-middle attacks, message modification, and resource misappropriation.
I'd suggest looking at this publication by the NIST. It provides some pretty useful information on Bluetooth security. The encryption protocol of bluetooth is E0 which is 128 bit.
Although bluetooth may not be the most secure protocol, you have to put things in perspective: Bluetooth has a relativity short transmit range. This means that if you were to use bluetooth keyboards in a building, a person would have to be in the same room or close to the room to actually do anything malicious.
Just because a certain technology is insecure, doesn't mean that it is useless.