  Transport and torque magnetometry measurements are performed at high magnetic
fields and low temperatures in a series of p-type (Ca-doped) Bi$_{2}$Se$_{3}$
crystals. The angular dependence of the Shubnikov-de Haas and de Haas-van
Alphen quantum oscillations enables us to determine the Fermi surface of the
bulk valence band states as a function of the carrier density. At low density,
the angular dependence exhibits a downturn in the oscillations frequency
between $0^\circ$ and $90^\circ$, reflecting a bag-shaped hole Fermi surface.
The detection of a single frequency for all tilt angles rules out the existence
of a Fermi surface with different extremal cross-sections down to $24$~meV.
There is therefore no signature of a camel-back in the valence band of our bulk
samples, in accordance with the direct band gap predicted by $GW$ calculations.
