Transportation from Barcelona to Bilboa

You've double-posted this question and ought to eliminate one. Your choices are essentially bus, train, and car. Train and car take about six hours, bus maybe an hour more.
Flying doesn't get you much in time savings since you probably have to change in either Madrid or Palma. I don't know why one would be more reliable than the other, except sometimes the Bilbao airport gets snockered in during the winter. Also the airport is up on a plateau east of the city so you'd have to make your way into town which eats up more time. The bus station is on the northwest fringe of New Bilbao, the train station is also in New Bilbao, but right across the Nervion from the Old Town. Both are about a mile from the Guggenheim. There's not much scenic to it until you get about to Vitoria - - for the most part is just flat and brown. Zaragoza is a pretty good stop if you can fit it in. Since you didn't ask, the Carlton is the grande dame of Bilbao hotels and for some goofy reason still peddles rooms for about a hundred bucks a night. It's right on the big ellipse which puts it a ten-minute walk to the museum and less than fifteen with an interesting walk to Old Town where all the good grub is.