Transverse stability of the drive beam is critical to plasma wakefield accelerators. A long, relativistic particle beam propagating in an overdense plasma is subject to beam envelope modulation and hosing (centroid displacement) instabilities. Coupled equations for the beam centroid and envelope are derived. The growth rate for beam hosing is examined including return current effects (where the beam radius is of order the plasma skin depth) in the long-beam, strongly-coupled, overdense regime.