Read the link in @j-g-faustus 's comment - very thorough. http://www.gammon.com.au/power - it starts with a stock board running at 50milliAmps and ends up at 0.002 milliAmps.
You will also need to find out the power consumption for your BT module - this may dwarf the power arduino's power consumption. The same goes for the LED.
Normal LEDs run at about (ballpark!) 20 milliamps - this means that on the coin battery mentioned by @Omer, 200milliAmp-hours/20 milliAmps = 10 hours of led light.
You can measure the power draw with a multimeter; stick your probes between the + of the battery and whatever the battery would normally connect to (you will have to disconnect the battery of course) - if using a 9v battery, plug in the negative, disconnect the positive, turning the snap connector 90 degrees; then you can put one probe on the battery, the other on the (open) snap connector. Measure Arduino awake + led on + BT connected and sending data. Measure again with everything off/idle/sleeping. Work out how much time it will spend in each state; this will give you an average number of milliamp-hours.