I will present a general method to construct bulk-deformed open topological string theories from Landau-Ginzburg models. The main ingredients in the construction are a "weak" version of deformation quantisation, and an application of the homological perturbation lemma. Together they allow to explicitly compute all bulk-deformed open topological string amplitudes at tree-level before tadpole-cancellation. The talk is based on work with N. Carqueville (arXiv:1104.5438).