how is the aluminium plate bonded to the PCB for best heat transfer?
Double-sided tape?
(I guess it's possible lol)
Epoxy?
They use a thermally conductive dielectric [usually epoxy and reinforced with glass(most of the time) or ceramics(occasionally) which varies between manufactures and pcb requirements]
How does it cope with differential expansion?
That would depend on what your requirements of your board. Are you talking about out-of-plane from vias (usually minimized by thicker copper plating, thinner board, materials) or delaminating of the layers?
Heatbeds usually don't have much of vias through the aluminum layer though, or are you just asking about the rest of the pcb?