Bluetooth sends information through radio waves. The reason the sound plays instantaneously is that radio waves move at the speed of light (technically they are the same thing as light), as well as the fact that the bluetooth chips are encoding and decoding the information very quickly.
The next question you might have might be, how is the sound so much better than something like, say, FM/AM radio? One is that the data is compressed into a digital format instead of analog like old school radio. Bluetooth is also a much higher frequency. This makes it worse for sending information long distances, but you can pack a lot more information into the signal, resulting in better quality audio. There’s also lots of little engineering things going on that help clean up issues you run into with wireless data transmission: interference, lost data, etc.
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