You rang?
The military charging process begins with preferral of charges. This is the formal preparation of a charge sheet and its signature by a military member with knowledge of the facts behind the charge (normally the accused's immediate commander). The accused is then served with a copy of the charge sheet by his commander. In the case of a general court-martial (a felony-level crime, which this would be), there is then what's called an Article 32 hearing, which is essentially a preliminary hearing, overseen by an experienced JAG, who reviews the legal sufficiency of the charges and makes recommendations on which if any charges should be pursued to trial (this process is frequently, but not always, waived by the accused). The Article 32 officer's recommendations are not binding - just advisory. The case is then presented to the General Court-Martial Convening Authority (normally the first general/admiral in the accused's chain of command, though in some instances a Colonel can be a GCMCA). The GCMCA formally decides what charges are referred for trial.
In terms of publicity, the military is kind of its own creature since it is in effect a relatively small court (in terms of caseload) that has worldwide jurisdiction. Relatively few military cases attract media attention. I actually sent someone to prison for life as a JAG for child molestation, but few people even on our base knew about it. Technically the existence of a court-martial is a matter of public record once charges are referred, but as a practical matter the military trial courts don't have a docket that is searchable by the public and so information about pending cases is only public if a reporter elects to file a FOIA request.
The Bergdahl case reminds me of one I handled when I was a military defense attorney, and it's a weird one. I had an old man come into my office who had deserted during the Korean War (not from the Korean theater - he had just walked away from his Army base after being sexually assaulted by his NCOIC). He had spent the next 50 years working off the grid, constantly afraid he would be arrested. He had never been married or had a job that didn't pay cash. I helped him turn himself in and the prosecutor let him off with an administrative discharge rather than prosecuting him. Very very odd.