This paper presents an approach for the design of globally exponentially stable hybrid attitude and gyro-bias observers on SO(3) x R-3. First, we propose a hybrid observer developed in a generic manner involving a generic family of potential functions with specific properties. Thereafter, we present a design method for such potential functions via an appropriate angular warping transformation applied to a new potential function on SO(3). This results in a hybrid observer that uses directly body-frame measurements of known inertial vectors.