Anything that avoids backtracking is a good idea, so if you can find an affordable open-jaws flight into Madrid and out of Barcelona, or vice versa. Personally, unless you have a really compelling reason for visiting the Guggeheim, taking at least 2 days out of your week to visit Bilbao isn't worth it. You say you want to "visit the Guggenheim and other sights." But there are really no other sights in Bilbao to see. I would spend, say, 4 days in Madrid (it's a big city, lots of museums, great nightlife) including one or both of the excellent day trips Deanna suggested, and 3 days in Barcelona.
I've never stayed in Paradors....too expensive for me....but they're usually off the beaten path, so not really accessible by public transit, at least in the bigger cities.
If you're going to go by train, reserve up to 62 days out at renfe.es for the AVE train between Madrid and Barcelona...otherwise, it'll cost an arm and a leg!
You'll find warm weather in early September, but likely only a slight lessening of the crowds. It's still tourist season in September and, in many parts of Spain, kids don't go back to school until mid-month.