For this particular trip I would suggest taking Amtrak back to Eugene. Take the ferry over to Oakland. The train leaves very late in the day and you will be in Eugene the next day.
+1 You don't even have to box your bike up these days, they hang the bikes in the baggage car, no removing pedals or turning bars just remove "anything that might fall off" It's all of a minute's ride from the ferry to Oakland station, I was a senior but I believe the regular ferry fare is <$10 and bikes are no problem. Caveat: don't arrive too early for the train, there is absolutely nothing to do around Oakland station.