Circular dichroism spectroscopy is an important tool for determining the structural characteristics of biomolecules, particularly the secondary structure of proteins. In this paper we propose a Bayesian model that estimates the covariance structure within a measured spectrum and quantifies the uncertainty associated with the inferred secondary structures and characteristic spectra associated with each secondary structure type. Furthermore, we used tools from Bayesian model selection to determine the best secondary structure classification scheme and illustrate a technique for comparing whether or not two or more measured protein spectra share the same secondary structure. Our findings suggest that it is not possible to identify more than 3 distinct secondary structure classes from CD spectra above 175 nm. The inclusion of data from wavelengths between 175 and 200 nm did not substantially affect the ability to determine secondary structure fractions.