I rode to Maupin from Portland awhile back via Estacada, the Clackamas River Hwy, Forest Rd 57 to Timothy Lake, briefly on Hwy 26 (busy/good shoulder), then Hwy 216 (very quiet) to Maupin. It was a really nice two-day trip, with great camping options before and around Timothy Lake, but maybe more than you had in mind just to go rafting. There's camping right in the Maupin city park, though, so you could do a fantastic excursion combining bikes and rafts.
You could check the Statewide transit schedules
to see if anyone gets you close; maybe a Portland-Bend service would drop you and your bike at the remote intersection of Hwy 26 and 216, but that would take some good persuasion, I'll bet.
Also get a copy of the Oregon state bike map; it shows general traffic levels and whether there's a shoulder; in my brief experience riding in the region around Maupin, there's not much traffic, and the few busy highways there are (26, 97, 197) have reasonable shoulders so it's kind of noisy but safe. But check first, there are exceptions.