OK I am done answering this question–after three tries in three different ways!
You can get the BSSID of the AP you are connected to via the WiFi object.
You can scan for APs via the WiFi object’s scan method but that does not return the BSSID for each AP.
If you want to go around the WiFi object, which is there to make things easier to use, and program to the TI CC3000 on a Core directly, then you can get the BSSID, but you will have to build locally from the source after you modify it using gcc. You will need to know what you are doing in order to do that.