I'm a solo kayaker and I hitched Westwater earlier this year... as well as a half dozen other runs and multi-day trips. My best advice is just talk to everyone: Folks at the put in. Folks on the river. Folks at the take out. I always managed to find someone with room on their roof rack or raft trailer to haul me and my kayak back to the put in, usually long before I reached the take out.
Be sure to pay your fair share of expenses including gas, the shuttle, and a tip for the shuttle driver if it's a multi-day trip. If it's a rafter who's giving you a ride, be sure to help them de-rig and load their gear. Make yourself useful! Work your ass off! People were amazingly nice and helpful to me, but I did everything I could to make it a win-win situation, not just charity.