Bluetooth shield/module for file transfer?
I would use an HC-05 (or HC-06 - there seems to be little difference) - You will need to do your own file transfer protocol - for small images, zmodem or xmodem (usual file-over-serial) are probably completely overly complex. You would also need your own app for the phone.

Alternatively, you could use a network (ethernet or wifi) addon on your arduino - I think I read the Arduino Yun has built in ethernet and wifi.http://arduino.cc/en/Tutorial/WebServer has a webserver, this could be adapted to accept uploaded files. You can then use a webbrowser on your phone (or indeed anywhere else!) to send the files. If you want to send from outside your local network, you may need to set up port forwarding on your router (google: port forward) - the port you want to forwards is 80.