The variogram is a basic tool in geostatistics. It expresses the variability between pairs of observations as a function of their separation vector. When a spatial process is isotropic, customary approaches to variogram modeling create an empirical variogram to which one fits a standard variogram model. We model standard variograms and a flexible class of discrete mixtures of Bessel functions from a Bayesian perspective. We further introduce a utility based variogram model choice criterion that is composed of a goodness of fit component and penalty term that encourages parsimony. Scallop catches in the Atlantic Ocean during 1993 serve as an illustrative data set, while an earlier 1990 data set from the same region supplies useful prior information.