We model the fastest moving (v_tot > 300 km/s) local (D < 3 kpc) halo stars using cosmological simulations and 6-dimensional Gaia data. Our approach is to use our knowledge of the assembly history and phase-space distribution of halo stars to constrain the form of the high velocity tail of the stellar halo. Using simple analytical models and cosmological simulations, we find that the shape of the high velocity tail is strongly dependent on the velocity anisotropy and number density profile of the halo stars --- highly eccentric orbits and/or shallow density profiles have more extended high velocity tails. The halo stars in the solar vicinity are known to have a strongly radial velocity anisotropy, and it has recently been shown the origin of these highly eccentric orbits is the early accretion of a massive (M_star ~ 10^9 M_Sun) dwarf satellite. We use this knowledge to construct a prior on the shape of the high velocity tail. Moreover, we use the simulations to define an appropriate outer boundary of 2r_200, beyond which stars can escape. After applying our methodology to the Gaia data, we find a local (r_0=8.3 kpc) escape speed of v_esc(r_0) = 528(+24,-25) km/s. We use our measurement of the escape velocity to estimate the total Milky Way mass, and dark halo concentration: M_200,tot = 1.00(+0.31,-0.24) x 10^12 M_Sun, c_200 = 10.9(+4.4,-3.3). Our estimated mass agrees with recent results in the literature that seem to be converging on a Milky Way mass of M_200,tot ~ 10^12 M_Sun.