We report molecular dynamics (MD) simulations of the aqueous interface of the hydrophobic [BMI][Tf2N] ionic liquid (IL), composed of 1-butyl-3-methylimidazolium cations (BMI+) and bis(trifluoromethylsulfonyl)imide anions (Tf2N-). The questions of water/IL phase separation and properties of the neat interface are addressed, comparing different liquid models (TIP3P vs TIP5P water and +1.0/-1.0 vs +0.9/-0.9 charged IL ions), the Ewald vs the reaction field treatments of the long range electrostatics, and different starting conditions. With the different models, the "randomly" mixed liquids separate much more slowly (in 20 to 40 ns) than classical water-oil mixtures do (typically, in less than 1 ns), finally leading to distinct nanoscopic phases separated by an interface, as in simulations which started with a preformed interface, but the IL phase is more humid. The final state of water in the IL thus depends on the protocol and relates to IL heterogeneities and viscosity. Water mainly fluctuates in hydrophilic basins (rich in O(Tf2N) and aromatic CH( BMI) groups), separated by more hydrophobic domains (rich in CF3(Tf2N) and alkyl(BMI) groups), in the form of monomers and dimers in the weakly humid IL phase, and as higher aggregates when the IL phase is more humid. There is more water in the IL than IL in water, to different extents, depending on the model. The interface is sharper and narrower (similar to 10 angstrom) than with the less hydrophobic [BMI][PF6] IL and is overall neutral, with isotropically oriented molecules, as in the bulk phases. The results allow us to better understand the analogies and differences of aqueous interfaces with hydrophobic (but hygroscopic) ILs, compared to classical organic liquids.