The metal-to-insulator transition in BaTiO_{3} is investigated using electrostatic doping, which avoids effects from disorder and strain that would accompany chemical doping. SmTiO_{3}/BaTiO_{3}/SrTiO_{3} heterostructures are doped with a constant sheet carrier density of 3×10^{14} cm^{-2} that is introduced via the polar SmTiO_{3}/BaTiO_{3} interface. Below a critical BaTiO_{3} thickness, the structures exhibit metallic behavior with high carrier mobilities at low temperatures, similar to SmTiO_{3}/SrTiO_{3} interfaces. Above this thickness, data indicate that the BaTiO_{3} layer becomes ferroelectric. The BaTiO_{3} lattice parameters increase to a value consistent with a strained, tetragonal unit cell, the structures are insulating below ∼125 K, and the mobility drops by more than an order of magnitude, indicating self-trapping of carriers. The results shed light on the interplay between charge carriers and ferroelectricity.