Adenoid cystic carcinoma (ACC) is a head and neck cancer that frequently originates in salivary glands, but can also strike other exocrine glands such as the breast. A key molecular alteration found in the majority of ACC cases is MYB gene rearrangements, leading to activation of the oncogenic transcription factor MYB. In this study, we used immortalised breast epithelial cells and an inducible MYB transgene as a model of ACC. Molecular profiling confirmed that MYB‐driven gene expression causes a transition into an ACC‐like state. Using this new cell model, we identified BUB1 as a targetable kinase directly controlled by MYB, whose pharmacological inhibition caused MYB‐dependent synthetic lethality, growth arrest and apoptosis of patient‐derived cells and organoids.