My own brief summary of the subject is in an nLab article. (This is a math/physics wiki, and I assumed that the reader already knows quantum mechanics, at least up to the point of knowing what a density matrix is and what it's good for.) There are references there, but you'll notice that they're all linked from the History section. (Part of the point of that section is to make it clear that the idea predates Caves, Fuchs, et al, although they certainly deserve credit for making it prominent.) I don't know any over-all exposition that I really like, although I will always like the one cited as Baez 1993, which is where I learnt about it (and in fact where I first learnt about density matrices). That article doesn't say ‘Bayesian’, but as I was already a Bayesian when I read it, and since I knew Baez to be a Bayesian, I naturally interpreted it so. If you interpret the probabilities in a different way, then you'll get a very different interpretation of quantum mechanics as a result!
Someday I want to write something for beginners, at the level of Eliezer's essays here (and in fact probably post it here too), but I haven't done that yet! Until then, Baez's piece is at the right level, but it doesn't address the things that LessWrongers specifically would want to see.
I'd like to try and flesh out the difference between your personal interpretation and (for example) QBism. In your nLab article you describe an objective Bayesian is someone who "who naturally thinks of Bayesian probabilities as reflecting knowledge rather than belief, betting commitments, etc". This suggests that it has to be knowledge about something; about some objective ontological process I assume. Is this ontological process still somehow "quantum" in nature? Is it perhaps a hidden variable of some kind? You didn't reply to my pr...
Sean Carroll, physicist and proponent of Everettian Quantum Mechanics, has just posted a new article going over some of the common objections to EQM and why they are false. Of particular interest to us as rationalists:
Very reminiscent of the quantum physics sequence here! I find that this distinction between number of entities and number of postulates is something that I need to remind people of all the time.
META: This is my first post; if I have done anything wrong, or could have done something better, please tell me!