The 1 1 Be(p,d) 1 0 Be reaction has been performed in inverse kinematics with a radioactive 1 1 Be beam of E/A=35.3 MeV. Angular distributions for the 0 + ground state, the 2 + , 3.37 MeV state and the multiplet of states around 6 MeV in 1 0 Be were measured at angles up to 16 o c m by detecting the 1 0 Be in a dispersion-matched spectrometer and the coincident deuterons in a silicon array. Distorted wave and coupled-channels calculations have been performed to investigate the amount of 2 + core excitation in 1 1 Be g s . The use of ''realistic'' 1 1 Be wave functions is emphasised and bound-state form factors have been obtained by solving the particle-vibration coupling equations. This calculation gives a dominant 2s component in the 1 1 Be g s wave function with a 16% [2 + 1d] core excitation admixture. Cross sections calculated with these form factors are in good agreement with the present data. The Separation Energy prescription for the bound-state wave function also gives satisfactory fits to the data, but leads to a significantly larger [2 + 1d] component in 1 1 Be g s .