We report modeling results for low-field mobility and velocity saturation in bilayer graphene based on a newly developed semiclassical transport Monte-Carlo simulator validated by comparison with momentum relaxation time (MRT) calculations. We show that remote phonons originating in the dielectric stack are expected to strongly affect the mobility, although assessing their actual influence at high inversion charge requires the development of an accurate model for dynamic screening. When the applied bias opens the energy gap, the mobility is significantly reduced. The saturation velocity is expected to be as high as 3×107 cm/s and less degraded than mobility by bandgap opening.