Members of the public visiting hospitalized patients undergoing nuclear medicine procedures or brachytherapy are exposed to radiation emanating from the patient. The radiation protection staff at the hospital is responsible for ensuring that the doses to these visitors are kept as low as is reasonably achievable and are maintained below applicable regulatory limits. These limits are normally expressed in terms of the effective dose to the visitor. Direct measurement of the effective dose, however, is not feasible, and the use of a quantity that provides a reasonable estimate, referred to as a surrogate, is required. This study used Monte Carlo radiation transport calculations to examine the feasibility of using bedside survey results, in units of roentgens per hour, as a surrogate for estimating the effective dose to a person who may be present at the survey location. The Monte Carlo code used in this work was MCNP Version 5. In these calculations, both the patient and the visitor were modeled using modified Medical Internal Radiation Dose anthropomorphic phantoms. Radioactive material that emitted monoenergetic photons was located in several of the patient's organs in turn, and the bedside exposure rates and the effective doses at the same location were calculated. The calculations were repeated for several visitor locations, both at bedside along the length of the bed, and at increasing distances from the bed. The ratios of the exposure rates to the effective dose rates at each location gave an indication of the utility of the exposure rate measurements in providing a reasonable estimate of the effective dose. The results indicated that the survey data provided estimates of the effective dose within recommended accuracy for many exposure situations, but underestimated the effective dose to the visitor for other situations, especially locations close to bedside and for lower energy radiations. Use of appropriate correction factors based on this work could improve the utility of the survey data for the underestimated situations, and the exposure rate data could still be used to estimate the dose to a visitor within recommended accuracy, provided the estimated dose does not approach too closely to the applicable limit.