  We completely describe the degree of the Gauss map of the theta divisor of
bielliptic Prym varieties. We characterize bielliptic Prym varieties whose
Gauss degree is the same as Jacobians. We also construct bielliptic Prym
varieties with a very low Gauss degree. In dimension $5$, we obtain a complete
description of the Gauss degree on the Andreotti-Mayer locus.
