This paper presents a finite-time bearing-only formation control scheme via finite-time estimation of agents' global orientations. For the orientation estimation, we propose a distributed estimation law and establish almost global finite-time convergence. We provide analysis for undirected and a class of directed sensing and communication graphs. A distributed bearing-only formation control law is then proposed based on the orientation estimation. We provide a rigorous analysis for almost global stability and finite-time convergence of the system to the desired equilibrium. Particularly, under the proposed bearing-only formation control strategy, the actual formation almost globally exponentially finite-time converges to the desired formation shape. Finally, numerical simulations are provided to support our proposed control method.