  In the framework of massive gravity with a de Sitter reference metric, we
study homogeneous and isotropic solutions with positive spatial curvature.
Remarkably, we find that bounces can occur when cosmological matter satisfies
the strong energy condition, in contrast to what happens in classical general
relativity. This is due to the presence in the Friedmann equations of
additional terms, which depend on the scale factor and its derivatives and can
be interpreted as an effective fluid. We present a detailed study of the system
using a phase space analysis. After having identified the fixed points of the
system and investigated their stability properties, we discuss the cosmological
evolution in the global physical phase space. We find that bouncing solutions
