A new measuring technique dedicated to bubble velocity and size measurements in complex bubbly flows such as those occurring in bubble columns is proposed. This sensor combines the phase detection capability of a conical optical fiber, with velocity measurements from the Doppler signal induced by an interface approaching the extremity of a single-mode fiber. The analysis of the probe functioning and of its response in controlled situations, have shown that the Doppler probe provides the translation velocity of bubbles projected along the probe axis. A reliable signal processing routine has been developed that exploits the Doppler signal arising at the gas-to-liquid transition: the resulting uncertainty on velocity is at most 14\%. Such a Doppler probe provides statistics on velocity and on size of gas inclusions, as well as local variables including void fraction, gas volumetric flux, number density and its flux. That sensor has been successfully exploited in an air-tap water bubble column 0.4m in diameter for global gas hold-up from 2.5 to 30\%. In the heterogeneous regime, the transverse profiles of the mean bubble velocity scaled by the value on the axis happen to be self-similar in the quasi fully developed region of the column. A fit is proposed for these profiles. In addition, on the axis, the standard deviation of bubble velocity scaled by the mean velocity increases with Vsg in the homogeneous regime, and it remains stable, close to 0.55, in the heterogeneous regime.