  Free-standing Bi$_2$Se$_3$ single crystal flakes of variable thickness are
grown using a catalyst-free vapor-solid synthesis and are subsequently
transferred onto a clean Si$^{++}$/SiO$_2$ substrate where the flakes are
contacted in Hall bar geometry. Low temperature magneto-resistance measurements
are presented which show a linear magneto-resistance for high magnetic fields
and weak anti-localization (WAL) at low fields. Despite an overall strong
charge carrier tunability for thinner devices, we find that electron transport
is dominated by bulk contributions for all devices. Phase coherence lengths
$\l_\phi$ as extracted from WAL measurements increase linearly with increasing
electron density exceeding $1 \mu $m at 1.7 K. While $\l_\phi$ is in
qualitative agreement with electron electron interaction-induced dephasing, we
find that spin flip scattering processes limit $\l_\phi$ at low temperatures.
