We report an all-optical atomic vector magnetometer using dual Bell-Bloom optical pumping beams in a Rb vapor cell. This vector magnetometer consists of two orthogonal optical pumping beams, with amplitude modulations at 85 Rb and 87 Rb Larmor frequencies respectively. We simultaneously detect atomic signals excited by these two pumping beams using a single probe beam in the third direction, and extract the field orientation information using the phase delays between the modulated atomic signals and the driving beams. By adding a Herriott cavity inside the vapor cell, we improve the magnetometer sensitivity. We study the performance of this vector magnetometer in a magnetic field ranging from 100 mG to 500 mG, and demonstrate a field angle sensitivity better than 10 µrad/Hz 1/2 above 10 Hz.