We report the observation of ferromagnetic resonance-driven spin pumping signals at room temperature in three-dimensional topological insulator thin films -- Bi2Se3 and (Bi,Sb)2Te3 -- deposited by molecular beam epitaxy on yttrium iron garnet thin films. By systematically varying the Bi2Se3 film thickness, we show that the spin-charge conversion efficiency, characterized by the inverse Rashba-Edelstein effect length (lambda_IREE), increases dramatically as the film thickness is increased from 2 quintuple layers, saturating above 6 quintuple layers. This suggests a dominant role of surface states in spin and charge interconversion in topological insulator/ferromagnet heterostructures. Our conclusion is further corroborated by studying a series of YIG/(BiSb)2Te3 heterostructures. Finally, we use the ferromagnetic resonance linewidth broadening and the inverse Rashba-Edelstein signals to determine the effective interfacial spin mixing conductance and lambda_IREE.