This is two totally different questions.
First, 'can you send ECG signal through Bluetooth?' Of course you can. You can send any digital data you want over Bluetooth.
Now, for the hard question. ECG signals are on the order millivolts, so of course you're going to have to have an amplifier. The other problem is that the frequency range of ECGs is around 0 to 150 Hz. Unfortunately, AC line frequency is right in the middle of this range, so you may need some notch filtering, but you don't want to filter out important signals. I suggest you do a google search of "ECG signal interfacing". There's plenty of information out there.