This might appear to be a long answer, but I'm trying to cover all possibilities.
I have yet to find any device that can realistically handle two Bluetooth connections at the same time, so I'm guessing that your phone is connected to the car via Bluetooth, which is why you cannot use Bluetooth to connect your iPod.
Does the car have a USB socket, possibly for power? If so, I would expect that port to provide an audio connection to your car's system. You would need to switch the audio input on the car's controls to the USB input (and make sure you select the correct one if there is more than one). What should happen when the car is receiving and playing the music from your iPod, is that if a call comes in on your phone, the car should automatically switch to the phone and pause the music. When the call is ended, the music automatically resumes.
If it's a modern car, I'll take a guess that it does not have a 3.5mm audio jack socket, which would allow you to connect from the iPod's headphone socket to the 3.5mm input jack.
Does the car have an FM radio? If so, another possibility is to buy an FM transmitter, designed to turn your iPod's headphone output into a radio signal. You then tune your car's FM radio to the same frequency as the transmitter and the iPod's music is sent via a low-powered radio signal to the car. Be aware though, that the audio quality is usually not as good as other methods.
Lastly (and Apple may not thank me for this one), have you considered putting your music onto your Android phone? There is software for Android and PC that acts almost the same way as iTunes.