There's a growing number of bicycle roadways but many take advantage of existing infrastructure like old railroad beds:
There's a bridge that's connected to the same bikeway:
It cost $5,000,000 to build. Though most folks appreciate the artfullness of it, there's plenty of people who believe the 5 million could have been spent in better ways, even bike people. I use it every day. It's nice for getting across one busy highway but there were lights that allowed you to cross before. I end up just waiting at a different set of lights at a more dangerous crossing anyway.
Another offshoot of that same bikeway has recently been extended right past the back of my building. In fact the building had to give up a few feet of its tiny parking lot to accommodate it. Great for me though, right? Not really. It's fenced off. I have to ride a few blocks on streets to get on it.
That's a common problem with the bike infrastructure here. There's only so many access points. To get anywhere useful you need to be comfortable riding on the streets anyway. I imagine an elevated system would have the same problem.
Instead of thinking of all streets as "automobile roads", we as a culture need to start seeing them as multi-purpose roads, - not just for cars.