Lateral conductivity and magnetotransport measurements were performed with SiGe single quantum well (QW) structures doped with boron in the QW. The conductivity at low temperatures (T) is shown to be due to hopping over B centers while at higher T, it is due to two-stage excitation: thermal activation of holes from the ground to strain-split B states are followed by hole tunneling into the valence band. The tunneling is due to a potential drop across the QW which is due to hole capture at surface states of the Si cap layer making the surface charged. The external potential applied across the QW essentially changes the lateral conductivity as well as the activation energy. The calculations of band profile, free carrier concentration in the QW and acceptor population, as well as an effect on the transverse electric field were carried out taking into account the charging of surface states.