If you really don't want to use an extra horse put the saw in a carrying case (or at least cover the bar with a plastic scabbard), cut a slot in the bottom of a large saddlebag you don't use anymore, and carry it by putting the bar through the slot, engine unit in the saddlebag.
Put gas, oil, tools, in the opposite saddlebag. Be a little off balance, but that could be corrected with a rock if it was a big issue.
It'd take a good sized saddlebag (depending on how big the saw/case is) but it should carry fine. Might be easier to just scabbard the bar instead of using a full case just so it'd fit in the saddlebag easier.
"Don't just feed it! Ride it!" And the People said "AMEN!"