The 300lb rating for the ladder is most likely a 'static' rating - ie a big fat guy can climb the ladder with the camper parked. Although I would be doubtful that the manufacturer did any sort of calculations and just had Bubba go climb it to test it. What you are suggesting would be a dynamic load - a load that is there while the camper is in motion. With it hanging way off the back, if you hit a dip or speed bump a little too fast, the effective load could easily exceed 300lbs due to the g-forces and leave your ladder and bike lying in the road.
I wouldn't do it.