The target asteroid of the OSIRIS-REx asteroid sample return mission, (101955) Bennu (formerly 1999 RQ36), is a half-kilometer near-Earth asteroid with an extraordinarily well constrained orbit. An extensive data set of optical astrometry from 1999 to 2013 and high-quality radar delay measurements to Bennu in 1999, 2005, and 2011 reveal the action of the Yarkovsky effect, with a mean semimajor axis drift rate da/dt=(-19.0±0.1)×10-4au/Myr or 284±1.5m/year. The accuracy of this result depends critically on the fidelity of the observational and dynamical model. As an example, neglecting the relativistic perturbations of the Earth during close approaches affects the orbit with 3σ significance in da/dtda/dt.The orbital deviations from purely gravitational dynamics allow us to deduce the acceleration of the Yarkovsky effect, while the known physical characterization of Bennu allows us to independently model the force due to thermal emissions. The combination of these two analyses yields a bulk density of ρ=1260±70kg/m3, which indicates a macroporosity in the range 40±10% for the bulk densities of likely analog meteorites, suggesting a rubble-pile internal structure. The associated mass estimate is (7.8±0.9)1010kg and GM=5.2±0.6m3/s2. Bennu's Earth close approaches are deterministic over the interval 1654-2135, beyond which the predictions are statistical in nature. In particular, the 2135 close approach is likely within the lunar distance and leads to strong scattering and numerous potential impacts in subsequent years, from 2175 to 2196. The highest individual impact probability is 9.5×10-5 in 2196, and the cumulative impact probability is 3.7×10-4, leading to a cumulative Palermo Scale of -1.70.