Referring to this, the lowest latencies achieved in Bluetooth audio streaming are around 30-40ms. Given the fact that Bluetooth physical layer data rate is of around 2-3 Mbps and today's Bluetooth chipsets support sufficiently high processing power, the source to playback device latencies should be much lower (e.g. within 10ms or so, even by keeping substantial buffering.)
The audio codecs like AptX claim to add latency by 1.8ms only.
What causes so high latency in Bluetooth audio streaming using Bluetooth A2DP profile?