The problem of constructing local bulk observables from boundary CFT data is of paramount importance in holography. We begin addressing this question from a modern bootstrap perspective. Our main tool is the boundary operator expansion (BOE), which holds for any QFT in AdS. Following Kabat and Lifschytz, we argue that the BOE is strongly constrained by demanding locality of correlators involving bulk fields. Focusing on ‘AdS form factors’ of one bulk and two boundary insertions, we reformulate these locality constraints as a complete, non-perturbative set of sum rules on the CFT and BOE data. We study the flat-space limit when the AdS form factor reduces to a flat-space form factor, and provide a phase-shift formula for it in terms of CFT data. In 2d, under certain extremality assumptions on the CFT, this formula leads to Watson’s equations for integrable form factors. We discuss the utility of bulk locality, in combination with crossing, for the conformal bootstrap.