Quantum sensing is considered to be one of the most promising subfields of quantum information to deliver practical quantum advantages in real-world applications. However, its impressive capabilities, including high sensitivity, are often hindered by the limited quantum resources available. Here, we incorporate the expected information gain (EIG) and techniques such as accelerated computation into Bayesian experimental design (BED) in order to use quantum resources more efficiently. A simulated nitrogen- vacancy center in diamond is used to demonstrate real-time operation of the BED. Instead of heuristics, the EIG is used to choose optimal control parameters in real time. Moreover, combining the BED with accelerated computation and asynchronous operations, we find that up to a tenfold speedup in absolute time cost can be achieved in sensing multiple surrounding 13C nuclear spins. Our work explores the possibilities of applying the EIG to BED-based quantum-sensing tasks and provides techniques useful to integrate BED into more generalized quantum sensing systems.