This paper reports an experimental and theoretical investigation on the electronic structure of bismuth selenide (Bi2Se3) up to 9 GPa. The optical gap of Bi2Se3 increases from 0.17 eV at ambient pressure to 0.45 eV at 8 GPa. The quenching of the Burstein-Moss effect in degenerate samples and the shift of the free-carrier plasma frequency to lower energies reveal a quick decrease of the bulk three-dimensional (3D) electron concentration under pressure. On increasing pressure the behavior of Hall electron concentration and mobility depends on the sample thickness, consistently with a gradual transition from mainly 3D transport at ambient pressure to mainly two-dimensional (2D) transport at high pressure. Two-carrier transport equations confirm the trapping of high-mobility 3D electrons, an effect that can be related to a shallow-to-deep transformation of donor levels, associated with a change in the ordering of the conduction band minima. The high apparent areal density and low electron mobility of 2D electrons are not compatible with their expected properties in a Dirac cone. Measured transport parameters at high pressure are most probably affected by the presence of holes, either in an accumulation surface layer or as minority carriers in the bulk.