As is often the case with obscure terms, the Jargon File has an answer:
[Unix: from runcom files on the CTSS system 1962-63, via the startup script /etc/rc] Script file containing startup instructions for an application program (or an entire operating system), usually a text file containing commands of the sort that might have been invoked manually once the system was running but are to be executed automatically each time the system starts up.
Thus, it would seem that the "rc" part stands for "runcom", which I believe can be expanded to "run commands". In fact, this is exactly what the file contains, commands that bash should run.