I used a KLR 650 for a few years. I highly recommend the moto shuttle if you have a bike. The KLR is a little heavy to put on a hitch rack IMO, so I would ride it separate and whoever I was floating with would drive the rig pulling the raft. A smaller dirt bike would be ideal. Depending on the length of the shuttle, I also bike it or hitch hike if there is enough traffic.
By the waterside I will lay my head.
Listen to the river sing sweet songs to rock my soul.