Quasi-periodic conductance fluctuations are observed in the low-temperature magneto-conductance of a bilayer graphene sample. The quasi-periodic nature of the fluctuations is confirmed by their Fourier power spectrum, which consists of just a small number of dominant frequency components. From an experimental study of these features, which are highly reminiscent of those reported previously for ballistic semiconductor quantum dots, we suggest that they are associated with the formation of an open quantum dot in the submicron graphene sample.