Abstract: A search for Standard Model Higgs bosons produced in association with a high-energy photon and decaying to b (b) over bar is performed using 133 fb(-1) of root s = 13 TeV pp collision data collected with the ATLAS detector at the Large Hadron Collider at CERN. The photon requirement reduces the multijet background, and the H -> b (b) over bar decay is the dominant decay mode. Event selection requirements target events produced by vector-boson fusion, the dominant production mode in this channel. Several improvements enhance the search sensitivity compared to previous measurements. These improvements include better background modelling and characterization, the use of a neural-network classifier, and an updated signal extraction strategy adopting a direct binned-likelihood fit to the classifier output. With these improvements, the Higgs boson signal strength is measured to be 0.2 +/- 0.7 relative to the Standard Model prediction. This corresponds to an observed significance of 0.3 standard deviations, compared to an expectation of 1.5 standard deviations assuming the Standard Model.