Checklists are used to aid the fulfillment of safety critical activities in a variety of different applications, such as aviation, health care or labour inspections. However, optimizing a checklist for a specific purpose can be challenging. Checklists also need to be trustworthy and user friendly to promote user compliance. With labour inspections as a starting point, we introduce the Checklist Construction Problem. To address the problem, we seek to optimize the content of labour inspection checklists in order to improve the working conditions in every organisation targeted for inspections. To do so, we introduce a hybrid framework called BCBR to construct trustworthy checklists. BCBR is based on case-based reasoning (CBR) and Bayesian inference (BI) and constructs new checklists based on past cases. A key novelty of BCBR is the use of BI for constructing new features in past cases. The augmented past cases are retrieved via CBR to construct new checklists, which ensures justification for the content of the checklists and promotes trust. Experiments suggest that BCBR is more effective than any other baseline we tested, in terms of constructing trustworthy checklists.