Only owner can enable Bluetooth on CyanogenMod
I'll say because CM based ROMs have Cyanogenmod as the base plus extra features in them. So you might wanna check them out. It will have all the base CM features. 
One good option to go with is Paranoid Android. 
Some other ROMs : Bliss Pop , Resurrection Remix. 
Try them and tell me what you find ! 
Good Luck !