Some good thoughts flying around here this afternoon. I got called away, but have just caught up.
The lack of mud or plant material either on his shoes or on the wheel arches would fit with just stopping on the bitumen and rolling the body out of the back and over the edge of the bridge. No going onto the mud at all, despite my previous theory about her being dumped down the bank at the end of Little Ugly Creek.
The evidence from the bail hearing is that she appears to have been put where she was found very soon after death, so whoever put her there wouldn't have gone off the road at all. Just kept an eye open for approaching headlights or car sounds (early hours of the morning would have been pretty deserted out there), stopped on the bridge, done the deed (which would have been fairly nerve-wracking I would think) then driven off, turned around, and gone home.
Hence no mud or plant material on shoes or wheel arches.