Re: Transporting a motor bicycle - on its side...
It shouldn't make any difference which side but you can expect some oil to go where it's not supposed to be if the bike is laid on its side for very long. Sounds as if you know what to expect and no, there is no other danger other than oil migration. Fuel is another consideration. I'd consider draining the tank before transporting a bike on its side. Just common sense.
Age and Treachery Will Always Triumph
Over Youth and Skill & "Charlie Don't Ride"