Yes, all cheap bluetooth module work fine with APM, but this one is for 3.3V input, APM telemetry voltage output is 5V, require a voltage drop and this setting: 57600,8,1,n.
I browsed through the pictures of this ebay-item, on the backside of the board there is text VCC 3.6---6, it would indicate voltage tolerance up to 6V ?? Or not? I have I similar board with the same texts but have not connected it yet so I'm curious...
see http://robotosh.blogspot.ca/2012/07/arduino-jy-mcu-bluetooth.html for some info on that Bluetooth Module.
It looks like it has a small voltage regulator on board, and some a series resistors in-line of tx from the Arduino to drop the voltage below 3.3V.
I meant to add that it should work fine with 5V of the APM.
[x] Hope bluetooth support will be added soon :-)
The app seems to be great, but i can't use it because i've Xbee. Thanks for your development!