We have searched for evidence of physics beyond the standard model in events that include an energetic photon and an energetic b-quark jet, produced in 85 pb-1 of (image found) collisions at 1.8 TeV at the Tevatron Collider at Fermilab. This signature, containing at least one gauge boson and a third-generation quark, could arise in the production and decay of a pair of new particles, such as those predicted by supersymmetry, leading to a production rate exceeding standard model predictions. We also search these events for anomalous production of missing transverse energy, additional jets and leptons (e, µ and τ), and additional b quarks. We find no evidence for any anomalous production of γb or γb+X events. We present limits on two supersymmetric models: a model where the photon is produced in the decay (equation found), and a model where the photon is produced in the neutralino decay into the gravitino LSP, (equation found). We also present our limits in a model-independent form and test methods of applying model-independent limits.