It is NOT a bluetooth keyboard issue but it IS a BLUETOOTH issue as it relates to IOS.
It has happened on my Ipad and the music played through the speaker, so it is NOT an earbud or headphone issue.
I do not have a bluetooth keyboard but I always use a bluetooth earpiece for phone conversations.
Both my Ipad Mini and my Iphone will, at any time, start to play a song AFTER I end a call.
It happens regularly...maybe once or twice a day out of 30 or 40 calls.
I have not been able to predict the event.
I was just in Apple and remarkably, no one has ever heard of this phenomena.
It has happened to my wife's Ipad (she has a bluetooth keyboard).
It has happened with Ios7, Ios 6 and Ios 5.
I have a bluetooh keyboard with my Mac Mini and my wife has a BT Keyboard with her Macbook and neither have ever spontaneosly started a song, so it IS an IOS issue.
There is no digital environment as complete as Apple but it saddens me that Apple has not onlyignored the isse, but has apparently gone out of their way to make sure no one in the organization admits to its existance.
It must be one **** of a software problem so entangled in code that they cannot find a fix.