  We confine a dense suspension of motile \textit{Escherichia coli} inside a
spherical droplet in a water-in-oil emulsion, creating a "bacterially"
propelled droplet. We show that droplets move in a persistent random walk, with
a persistence time $\tau\sim 0.3\, {\rm s}$, a long-time diffusion coefficient
$D\sim 0.5\, \mu {\rm m}^2/{\rm s}$, and an average instantaneous speed $V\sim
1.5\, \mu{\rm m/s}$ when the bacterial suspension is at the maximum studied
concentration. Several droplets are analyzed, varying the drop radius and
bacterial concentration. We show that the persistence time, diffusion
coefficient and average speed increase with the bacterial concentration inside
the drop, but are largely independent of the droplet size. By measuring the
turbulent-like motion of the bacteria inside the drop, we demonstrate that the
mean velocity of the bacteria near the bottom of the drop, which is separated
from a glass substrate by a thin lubrication oil film, is antiparallel to the
instantaneous velocity of the drop. This suggests that the driving mechanism is
a slippery rolling of the drop over the substrate, caused by the collective
motion of the bacteria. Our results show that microscopic organisms can
transfer useful mechanical energy to their confining environment, opening the
way to the assembly of mesoscopic motors composed of microswimmers.
