That should be very easy with an Arduino + NFC (or RFID) reader/shield + Bluetooth module/shield.
Here is a cheap NFC reader (based on the MFRC522 chip) from ebay ~$6 link and it uses SPI for communication, also here is a blog post that shows how to use it with an arduino link
for the bluetooth, the easiest way is to use a serial module like this ~$5 just google "arduino + HC-06" and you will find many results showing how to use it.
then you need to write the code that read data from SPI and sends it over serial.
here is another NFC reader (based on the same chip MFRC522) link but the module exposes the serial pins UART instead of SPI, so technically you can wire this directly to the bluetooth module (RX-->TX and TX-->RX) but you need to match the baudrate and other serial settings between the two
Some bluetooth modules can be programmed over serial (simple commands to change default settings like Name, PIN code and speed) but i have used one that didn't allow me to change default speed (9600).
also check to make sure voltages match 5v or 3.3v or use something like a voltage divider.