iPhone audio bluetooth
Here's the relevant passage from the 2012 Prius C's user manual:

Before using the Bluetooth® audio/phone, it is necessary to register a Bluetooth® device in the system. Follow the procedure below to reg-
ister (pair) a device:
Press the tune knob and select “Bluetooth” using the tune knob.
Press the tune knob and select “Pairing” using the tune knob.
A passkey will be displayed.
Input the passkey into the device.
Select “Yes” to register the device. Depending on the type of device, it may register automatically.
If a Bluetooth® device has both music player and cellular phone func-
tions, both functions will be registered at the same time. When delet-
ing the device, both functions will be deleted at the same time.
If the off-hook switch is pressed and the “PHONE” mode is entered
when no phones have been registered, the registration screen will be
automatically displayed.

Basically, the music should just work. Try re-setting it up again and report back by commenting under this answer.