An elevated bikeway would be ridiculously cost prohibitive. I'm a big bike proponent, but I sure wouldn't want to pay for that.
Recently, I was involved in community input on a road project in my town. One of the options was a pedestrian/bike friendly bridge over the existing two lane road. Cost of that bridge was $1.2M and that was 4 years ago. The resulting design, of which one of the goals was traffic calming was to create 3 roundabouts and put wide shoulders on the roadway between them. Previously, there was no shoulder and this was a non-bike friendly roadway although it was bordered by a heavily used multi-use path. Now, the traffic goes slower, there are far less accidents, fast cyclists can safely ride on the road (shoulder) where they couldn't before and slower pedestrian traffic/slower cyclists/inline skaters etc... can use the associated multi use paths. The cost for this almost 1.5 miles of roadway was $1.2M - or about the same at the one bike friendly pedestrian bridge. I like the solution that was implemented much better and there are no stop lights either. On top of that, there wouldn't be the eyesore that an elevated bikeway would be (nor the climb up to it).
It doesn't take much to make a roadway be quite bike friendly. Just putting wide shoulders in place and keeping the intersections under control (roundabouts are great) makes an immense difference.
Riding on a heavily used MUP is just plain dangerous if you have any speed much over walking speed. You also get the bonus danger of having the intersection issue mentioned numerous times above.
J.