The Bluetooth available in your CTS is only for phone calls - it's not possible to stream audio through it from any device. Your only choices are to use an AUX cable, the OEM cable from GM (for iPhone/iPod/iPad only, that is), or removable USB storage.
Mine has a 6 CD changer and it plays mp3s. You can burn an awful lot of mp3s to 6 CDs and it's very convenient, if a bit old fashioned. Just remember to burn a "Data Disk" of mp3s as opposed to an Audio Disk. As mentioned elsewhere, it helps to have all the correct tags on the mp3s so you can see titles, etc.