First, a "biker" rides a V twin with loud pipes, wears leather, and has tattoos.
OK, now that's out of the way.
Changing the laws, putting out lots of PSAs on what the laws are, and stepping up enforcement on reckless and obviously stupid actions for all users would likely raise the level of compliance.
The separate facilities only folks are way off base - how many miles of roads are there in the US? Can't lane them all. Would require condemning billions of acres of people's yards!
Simply making the roads rational and educating people as to how they're rational, and enforcing the crap out of the safety related aspects of behavior would do it.
Much of the problem seems to spring from our cavalier presentation of driving in general on TV, where it's something that doesn't take any attention and anyone can do fancy trick driving. And the victims are better next episode. Cycling generally gets presented as either strolling or sport, not as a useful activity for actually doing things.
Same thing for motorcycles - very few utility motorcyclists out there, so the equipment and public perception is that they're a recreational toy for most, an escape vehicle for a certain number of thug bikers, and something different for the brightly clad dual-sport tourists. Nobody knows what to think of me with boxes lashed on heading for FedEx.
I expect nothing to happen that's useful. It's the American way.