Bubble formation in liquids is frequently observed in nature and applied in various industrial processes. These include pool and flow boiling for thermal management systems, where bubbles may form asymmetrically at narrow slits and in convective flows. While previous studies have focused on symmetric bubble formation at circular orifices, the dynamics of asymmetric bubble formation remains poorly understood. Here, we experimentally investigate bubble formation at rectangular orifices and examine the effects of the orifice size and aspect ratio and the gas flow rate on the bubble size. The asymmetric bubble shape evolution at the rectangular orifice is analyzed, and we find that the size of the bubble neck is controlled either by the orifice size or by the capillary length. Based on these findings, we develop a static force balance model to predict the bubble size in the quasi-static regime, where the roles of Bond number and aspect ratio are identified. The bubble size evolution in the dynamic regime is further understood by introducing a Weber number that evaluates the effect of the virtual mass force induced by gas flow. Our study provides physical understanding of the dynamics of asymmetric bubble formation and guidance to predict the bubble size at asymmetric orifices.