The classical trajectory of an initially unbound positron within the electric field of an antiproton and a uniform magnetic field is simulated in three dimensions. Several simulations are run incorporating experimental parameters used for antihydrogen production, which has been achieved by two different groups [M. Amoretti, Nature (London) 419, 456 (2002); G. Gabrielse, Phys. Rev. Lett. 89, 213401 (2002)]. The simulations indicate that temporary bound states of antihydrogen can form at positive energies, where the energy of the system is defined to be zero when the positron and antiproton are at rest with infinite separation. Such quasibound states, which form only when the magnetic field is present, are typically smaller than in a dimension perpendicular to the magnetic field. An analytical model is developed for a formation cross section, and it is found that quasibound states may form more frequently than stable Rydberg states.