Jet boating would be cool, but it's expensive. The upside is you get to run up the river and it only takes a couple hours, making for a shorter drive home. Salmon River Lodge is one company that does jet boat shuttles - their Lodge is just across the river from Corn Creek.
(note the "Jet Back Info" in the document
As for vehicle shuttles - the less vehicles and more people per vehicle the less expensive the shuttle. We've used River Shuttles in the past and they're great.
River Shuttles Salmon, Idaho - Shuttle Rates & Info
Either way, the shuttle tends to be the most expensive part of a private trip.