Let a pedal, padded with a section of pool noodle, rest on a rung to support weight, then firmly fasten to the ladder. Pool noodles are available at Dollar stores for a...$1. They can be used on ladder verticals and bike frame to protect. I'd use 1" wide tie down nylon straps rather than bungie cords. Since your ladder is usually rated for at least a 220 lb. person, I think it can handle a 30-50 lb. bicycle. You may have to loosen handlebars so they don't rub on RV back. Most bikes don't have a rear fender, which couldn't support the weight of the bike anyway.
When using straps, make sure at least one also loops around a higher rung to help support weight. While a bike isn't that heavy, the violent motions of the ladder so far behind your rear axle can make for pretty dramatic forces.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI