Graphene quantum dots provide promising platforms for hosting spin, valley, or spin-valley qubits. Taking advantage of the electrically generated band gap and the ambipolar nature, high-quality quantum dots can be defined in bilayer graphene using natural p-n junctions as tunnel barriers. In these devices, demonstrating the electrical tunability of the p-n junction barriers and understanding its physical mechanism, especially in the few-electron regime, are essential for further manipulating electron's quantum degrees of freedom to encode qubits. Here, we show the electrostatic confinement of single quantum dots in bilayer graphene using natural p-n junctions. When the device is operated in the few-electron regime, the electron tunneling rate is found to be monotonically tuned by varying gate voltages, which can be well understood from the view of manipulating the p-n junction barriers. Our results provide an insightful understanding of electrostatic confinement using natural p-n junctions in bilayer graphene, which is beneficial for realizing graphene-based qubits.