AFAIK iOS 7 supports BLE but it does not support SPP. Any chance to have virtual serial port on iOS just like it's UART to send bytes to BLE module and receive bytes from BLE module? I've purchased cc2540 and cc2541 TI's ble modules, will they work as virtual serial port on iOS? What about FRCOMM?
By "ble module" do you mean something like the HM-10 or HM-11 etc? If that's what you're talking about then you can just use the SDK from RedBearLab (they use the same chips from TI).
in their BLEDefines.h just change the defines to
#define RBL_SERVICE_UUID "FFE0" #define RBL_CHAR_TX_UUID "FFE1" #define RBL_CHAR_RX_UUID "FFE1"
This should get you connected to the module. Then from there they have some examples that are pretty straight forward to figure out.
And yes you communicate with it via a serial port.