Gamow-Teller and dipole transitions to final states in B13 were studied via the C13(t,He3) reaction at Et=115AMeV. In addition to the strong Gamow-Teller transition to the B13 ground state, a weaker Gamow-Teller transition to a state at 3.6MeV was found. This state was assigned a spin-parity of 3/2- by comparison with shell-model calculations using the WBP and WBT interactions which were modified to allow for mixing between nω and (n+2)ω configurations. This assignment agrees with a recent result from a lifetime measurement of excited states in B13. The shell-model calculations also explained the relatively large spectroscopic strength measured for a low-lying 1/2+ state at 4.83MeV in B13. The cross sections for dipole transitions up to Ex(B13)=20MeV excited via the C13(t,He3) reaction were also compared with the shell-model calculations. The theoretical cross sections exceeded the data by a factor of about 1.8, which might indicate that the dipole excitations are "quenched". Uncertainties in the reaction calculations complicate that interpretation.