© 2014 American Physical Society. We investigate the effect of potential barriers in the form of step edges on the scattering properties of Bi2Se3(111) topological surface states by means of large-scale ab initio transport simulations. Our results demonstrate the suppression of perfect backscattering, while all other scattering processes, which do not entail a complete spin and momentum reversal, are allowed. Furthermore, we find that the spin of the surface state develops an out-of-plane component as it traverses the barrier. Our calculations reveal the existence of quasibound states in the vicinity of the surface barriers, which appear in the form of an enhanced density of states in the energy window corresponding to the topological state. For double barriers we demonstrate the formation of quantum well states. To complement our first-principles results we construct a two-dimensional low-energy effective model and illustrate its shortcomings. Our findings are discussed in the context of a number of recent experimental works.