I know that the book which first exposed the public to both of the pirates, A General History of the Pyrates, supposedly based it's biographies of both women heavily off of the trial, but does the documentation still survive today? If it does, is there anywhere where one can read it or is it only available in archives?
And, presuming it does exist, does it generally correspond to the what A General History of the Pyrates says about them? Or there any interesting or contradictory facts which the book left out?
Question 1: Does the trial account still exist?
Answer: Yes.
Question 2: Is it available?
Answer: Yes. They put the court transcript of the trial (which are more or less "general meaning" transcripts and not the word-for-word transcripts we think of today...you try writing fast with loose ink like they did back then) into print and published copies of it (it was popular reading material). You can probably find it through some of the 18th-century print databases colleges have access to, or, go to a library and find a particular book collection, British Piracy in the Golden Age: History and Interpretation 1660-1730 a 4-volume set which reprints many period sources and trial accounts of pirates (you'll want volume 3, The Tryals of Captain John Rackam and other Pirates... (1720)). The two female pirates were tried along with other pirates, including their fellow crew members and another captured pirate, Charles Vane.
Question 3: Is Charles Johnson's version of it accurate per the trial accounts?
Answer: Generally, a hard no. Specifically... Anne Bonny and Mary Read had a career that lasted a total of 59 days. Johnson's depiction of that has at least some undocumented/fictional aspects to it. The portions of Johnson's portrayal before Bonny, Read, and Rackham stole a sloop out of Providence (for the two ladies anyway) are highly fictional. Johnson practiced what we call "factual fiction" today, basically mixing in fiction with facts for a host of reasons (including setting up a good narrative that would appeal to audiences who would buy his book). The idea of a woman disguised as a man at sea was interesting and appealing to many back then, so Johnson dressed it up for his audience.
Sounds like you have an interest pursuing some more pirate history. Might I recommend 1: following my blog, "Colonies, Ships, and Pirates" http://csphistorical.com/ and 2: perusing my recommended reading list for pirate history click here if you want to pursue pirate history further? I would highly recommend the book about women pirates that is on the list.
Paging /u/davidaop, our pirate expert, to help with this one.