Looks like you're already following the One Big Law of becoming a good writer: Write! :-)
So, with that out of the way, I have a few ideas to contribute. These are in no particular order though they are interrelated. And, of course, all standard disclaimers apply:
1) Find a local writing group to join that can critique your work. You say you miss feedback, so go get some. The key to this is getting the right writing group. Many are self-congratulatory groups of folks having fun hanging out and pretending to be artistes. You'll never hear a bad word out of them. Others are outlets for petty tyrants to boost their own self-worth by cutting down everyone else. You'll never hear a good word out of them.
What you want are a group of honest, constructive people that can tell you what they liked and what they didn't like -- and then can tell you why.
2) Read writing books. Look around at some of these "best writing book" lists people put out or elicit on sites like this. Pretty soon, you start to see the same subset of books show up over and over. Orson Scott Card's Characters and Viewpoint, for instance, if you're doing fiction. Have a look at some of those, and start in on one that interests you and addresses an area where you think you're weak.
3) Slice your writing into elements, rate each element, then pick one to focus on. By elements, I mean things like voice, characterization, pace, setting, clarity, and so on. Obviously my list is in the vein of fiction, but you get the idea. When you rate yourself on these elements, look for worst and the best.
Then, pick one or two, and study it, practice it, and polish it. For those you rate the worst, you're looking to improve them to the point where it doesn't damage your writing. If you're lucky, you'll start to "get it" and it could turn into a good thing in your writing. Or at least stop the bleeding.
For the best, these are the elements where your talents lay. You want to practice them, polish them, and play with them -- these are the elements that will make your writing shine and give it star power.
Final note on that before moving on: you don't have to be great at every element. Very possibly, you can't. JJR Tolkien was a master at creating mythical worlds, but his plots were fairly straightforward. HP Lovecraft's still around a hundred years later because he could narrate imagery that would sink its claws in your mind -- but he couldn't write dialog with a gun to his head. I read somewhere that out of a million-some published words he only wrote about 5000 of dialog. And those are... painful to read, in a bad way.
4) Look to the masters. You mentioned Bill Bryson and Christopher Hitchens. Two parts to this idea:
a) Read their stuff with "a writer's eye". See if you can identify what it is that makes you like them. Then, figure out what they do and how they do it that makes it so appealing. I'm not talking about in a broad sense, especially not at first. Take a single sentence, or bit of dialog, or paragraph that really grabs you, and figure out how they did it. Or at least figure out what they did. Explicitly defining it will help you put tools in your toolbox.
b) Sit down, pretend you are that author - like you're an actor playing them in a movie - and write as if you are them. Write what they would write, if they were sitting in that spot instead of you. I'm sure that plenty of people will be critical of this idea. After all, as a writer you want to find your own voice, not be a pale imitation of the other guy. But I do think it's useful sometimes. When you do this, you use those tools you've discovered in a way that flows, uninhibited by yourself and all the thousands of other possibilities of what you could put on paper. And in the process, you're actively learning to use those tools in a way that boosts your own writing. It's like training wheels.
5) Write some more. Or, so this has already been covered, but I'll repeat it here. It's a good one to end on. In some article I read, they claimed you can't really be a good writer until you've written a million words. The more I write, the more I believe them.
