A white wall rocket cultivar, designated 40-0801185-B, is disclosed. The invention relates to the seeds of white wall rocket cultivar 40-0801185-B, to the plants of white wall rocket cultivar 40-0801185-B, and to methods for producing a white wall rocket plant by crossing the cultivar 40-0801185-B with itself or another white wall rocket cultivar. The invention further relates to methods for producing a white wall rocket plant containing in its genetic material one or more transgenes and to the transgenic white wall rocket plants and plant parts produced by those methods. This invention also relates to white wall rocket cultivars or breeding cultivars and plant parts derived from white wall rocket cultivar 40-0801185-B, to methods for producing other white wall rocket cultivars, lines or plant parts derived from white wall rocket cultivar 40-0801185-B and to the white wall rocket plants, varieties, and their parts derived from the use of those methods. The invention further relates to hybrid white wall rocket seeds, plants, and plant parts produced by crossing cultivar 40-0801185-B with another white wall rocket cultivar.