An accelerated molecular dynamics procedure is developed and employed to investigate the onset of dislocation mobility in the prototypical system bcc Nb, which has several elastic and dislocation anomalies. The procedure combines constant-strain molecular dynamics, using thoroughly validated by us embedded-atom method potential, and hyperdynamics, using a global bond-boost potential. We demonstrate that the method enables nucleation of critical kink-pairs and the determination of the Gibbs energy of kink-pair formation \Delta G_kp(\tau ,T) as a function of experimentally-accessible shear stresses \tau  at different temperatures T < 100K. From \Delta G_kp(\tau ,T), the stress dependences of the entropy and the enthalpy of kink-pair formation are obtained using standard thermodynamic relations. The applicability of the method to other systems and stress-driven processes is also discussed.