We have studied, through detailed time- and space-resolved spectroscopies and numerical modeling, decay kinetics and spatial transport of free excitons confined near GaAs/Al_0.3Ga_0.7As heterointerfaces. We find that free excitons in bulk structures become readily localized by the conduction and valence bandbending at these n-p heterointerfaces. These excitons are thus quasi-two-dimensional and highly polarized in the growth direction, and give rise to a distinct, near-edge PL emission termed the H-band. We find these exciton dynamics to be completely analogous to the Quantum-Confined Stark Effect (QCSE), with excitonic transport which is extremely sensitive to the heterointerface electronic structure. We measure a 1.8-K quasi-2D exciton mobility of ~ 300,000 cm²/V-s.