Six axis force-torque sensors are commonly attached to the wrist of serial robots to measure the external forces and torques acting on the robot's end-effector. These measurements are used for load identification, contact detection, and human-robot interaction amongst other applications. Typically, the measurements obtained from the force-torque sensor are more accurate than estimates computed from joint torque readings, as the former is independent of the robot's dynamic and kinematic models. However, the force-torque sensor measurements are affected by a bias that drifts over time, caused by the compounding effects of temperature changes, mechanical stresses, and other factors. In this work, we present a pipeline that continuously estimates the bias and the drift of the bias of a force-torque sensor attached to the wrist of a robot. The first component of the pipeline is a Kalman filter that estimates the kinematic state (position, velocity, and acceleration) of the robot's joints. The second component is a kinematic model that maps the joint-space kinematics to the task-space kinematics of the force-torque sensor. Finally, the third component is a Kalman filter that estimates the bias and the drift of the bias of the force-torque sensor assuming that the inertial parameters of the gripper attached to the distal end of the force-torque sensor are known with certainty.