The Ramsey sequence is a canonical example of a quantum phase measurement for a spin qubit. In Ramsey measurements, the measurement efficiency can be optimized through careful selection of settings for the phase accumulation time setting, τ. This paper implements a sequential Bayesian experiment design protocol in low-fidelity Ramsey measurements, and its performance is compared to a previously reported adaptive heuristic protocol, a quantum phase estimation algorithm, and random setting choices. A workflow allowing measurements and design calculations to run concurrently largely eliminates computation time from measurement overhead. When precession frequency is the lone parameter to estimate, the Bayesian design is faster by factors of roughly 2 and 4 and 5 relative to the adaptive heuristic, random τ choices and the quantum phase estimation algorithm respectively. When four parameters are to be determined, Bayesian experiment design and random τ choices can converge to roughy equivalent sensitivity, but the Bayesian method converges 4 times faster.