Isn't BT 2.4GHz? It is also very low power (few milliwatts I think) so it's a good deal less likely than e.g. a mobile phone (variable power up to some 500mW) to affect any given piece of avionics.
I can say from personal experience that RF immunity between different pieces of installed equipment isn't something which gets exhaustively checked even in certain brand new planes, so I wouldn't do an ILS in real IMC with anything like that switched on.
However my view is that interference with avionics would be extremely unlikely.