A novel garden bean cultivars, designated HMX4129 is disclosed. The invention relates to the seeds of garden bean cultivars HMX4129 to the plants of garden bean line HMX4129 and to methods for producing a bean plant by crossing the cultivars HMX4129 with itself or another bean line. The invention further relates to methods for producing a bean plant containing in its genetic material one or more transgenes and to the transgenic plants produced by that method and to methods for producing other garden bean lines derived from the cultivars HMX4129.