Bluetooth does not have one specific frequency at which it works. Via bluetooth.com :
Bluetooth technology works in the unlicensed industrial, scientific and medical (ISM) band from 2.4 to 2.485 GHz, using an extended spectrum, frequency hopping, full duplex signal with a nominal speed of 1600 jumps per second.
... an adaptive hop among 79 frequencies with 1 MHz intervals gives a high degree of noise immunity and also provides more efficient transmission within the spectrum.
Thus, the use of frequencies will be widespread even for one connection with one device. There are hardware on the market, such as Ubertooth , that can perform packet captures and spectrum analysis .
As far as I know, iOS does not offer an API to find out this information. OS X works at some level, perhaps through the SPI or IOBluetooth API, because Apple Hardware Tools (search for "Bluetooth") offers a way to monitor the use of Bluetooth Bluetooth devices in OS X.
As for your desire to detect movement through the Doppler effect on the radio, my instincts say that it will be very, very difficult to do. I don’t know how the exact mathematics will look behind, but you will want to study what effect of Doppler on the transmission at the frequency of 2.4 GHz will be as a result of low and moderate speeds. (A higher speed or relative speed of, say, several tens of miles per hour, will quickly cause Bluetooth to use the wrong radio equipment due to the low transmit power.)