Master protocol designs allow for simultaneous comparison of multiple treatments or disease subgroups. Master protocols can also be designed as seamless studies, in which two or more clinical phases are considered within the same trial. They can be divided into two categories: operationally seamless, in which the two phases are separated into two independent studies, and inferentially seamless, in which the interim analysis is considered an adaptation of the study. Bayesian designs are scarcely studied. Our aim is to propose and compare Bayesian operationally seamless Phase II/III designs using a binary endpoint for the first stage and a time-to-event endpoint for the second stage. At the end of Phase II, arm selection is based on posterior (futility) and predictive (selection) probabilities. The results of the first phase are then incorporated into prior distributions of a time-to-event model. Simulation studies showed that Bayesian operationally seamless designs can approach the inferentially seamless counterpart, allowing for an increasing simulated power with respect to the operationally frequentist design.