Apple designed the AirPort base stations to only "extend" a wireless signal....using wireless only..... from another Apple base station.
Is your main base station another Apple router?
If yes, what model do you have?
If your main router is provided by another manufacturer, it would be extremely unlikely that the AirPort could "extend" the signal using wireless only.
I cannot say that it is impossible because I have not tested this with your model of BT device, but I would be extremely surprised if it worked.
If you have already tried to configure the AirPort to connect using wireless only....and are receiving error messages to the effect of the "network cannot be extended", the AirPort and BT products are not compatible for the purpose that you need.
You might want to confirm with the folks at an Apple Store....if you have one in your area....since they will be familiar with the Internet Service Providers in that region.