A Bluetooth device that will send data to a mobile phone
This easiest way to do this is to buy a bluetooth module which has serial port profile built-in to its firmware (Roving networks/ panasonic etc have such modules). Assuming your "device" has a microcontroller, the microcontroller could communicate to the BT module via some communication interface (say UART) to transmit and receive data. At the mobile phone end, you need to write an App which will connect and pair with the BT module in your device and once it establishes a stream, your App can transmit and receive data with your device.

This is quite straightforward, I was able to do this and transfer files from my device to an android phone in a week of tinkering.