Welcome!
I, too am unfamiliar with the options in that region, but most of the big regional trails - at least the ones I've investigated in detail - have bike related shuttle service, or bike-compatible public transportation options. I'd start with the trail's
associated website. In the case of other trails, these frequently have links to transportation and other options.
That trail looks pretty sweet from the tiny bit of Googling I did. Have you considered the possibility of riding it in both directions as a bike overnight kind of thing? Depending on fitness level, I imagine that could make a beautiful 2-4 day ride.
In any event, I wish you luck in your preparations and would love to hear more about your trip!