Yes, the 2010 Audi A4 has Bluetooth as a standard feature. However, the Bluetooth in the 2010 model only supports hands-free calling and voice recognition. It will not support Bluetooth audio streaming.
If you want to play your favorite tunes, you still have a few options. You can always use a 1/8th inch thick audio jack and plug your phone into the auxiliary port. Alternatively, you can buy a Bluetooth car kit, which typically retails for about $15 to $20. It’s easy to install, uses radio waves to work, and is generally an easy-to-use option.