This paper investigates the bearing-based formation control problem where the linear velocities and heading angles of leaders are time-varying. Different from traditional bearing-based formation control methods where each follower needs to acquire complete and time-varying velocities from the leaders, the time-varying linear velocities of the leaders are unknown to all followers in this paper. The uniqueness of the target formation is guaranteed by $n_l$ leaders moving in synchrony. Relying on the upper bound of the leaders' velocities and their heading angles obtained through communication, this paper proposes a bearing-based formation control algorithm for unicycle-modeled followers, achieving the desired geometric configuration of the target formation. The asymptotic stability of the closed-loop system is proved using the Lyapunov's theorem, and simulation results validate the effectiveness of the proposed formation control law.