Wise Clock 4 can now hold a Bluetooth module outside of the XBee socket, as shown in the pictures below.
The communication with the BT module uses SoftwareSerial on pins D20/PC4 (Tx) and D21/PC5 (Rx).
The module is powered with 3V3 and the Rx line is level-shifted.
I bought a few of these Bluetooth modules from different sources, mostly ebay. Some of them did not work: my PC's Bluetooth could not "discover" them. Once SMD-soldered to the board, it is very difficult to figure out what's wrong and even de-solder and remove them. My advice for anyone using these modules is to check them before soldering them to any board/breakout. An easy way to do this is to solder wires on pins 12 (Vcc) and pin 13 (ground), as shown in the photo below (left), power with 3.3V, then try to pair it with a Bluetooth host (PC, Android; iPhone won't work since it requires an Apple-approved chip).
The module's relevant pins are shown in the diagram below (photo from ebay seller):
I did not test this myself (the experiment may cost about $7), but it seems that these Bluetooth modules only tolerate approx 3.3V and powering with 5V will fry them.
If you already have an Wise Clock 3/4 and want to add Bluetooth functionality (simultaneous to WiFi or XBee), you can add this module to the clock. Connections are through 4 wires: Rx/Tx go to D20/D21 (pins 26 and 27 of the processor), VCC to 5V, GND to ground. Note that this module has on-board power adapter for 3.3V and level-shifter for the logic lines.