Your interpretation (1) could be somewhat close to the meaning if it were "Don't bother to ask ...", but the meaning of "Don't bother asking" is more like:
Don't waste your time asking anyone. The answer should be clear to you. You should know what to do. (In the text, "you" should simply drop out of the program, because you're just not cut out for it.)
I followed your link on Academia Stack Exchange to the original blog post. Here is the relevant part:
... I'm just telling you what I saw in my own mid-tier Ph.D. institution, and what I've heard from other people from other Ph.D. programs in my field. Here goes:
My first semester in grad school, my M.A. advisor laid it out for to me: "If you get a B in a grad school class, you should ask the professor whether you should consider dropping out of the program. If you get a C, don't bother asking."
(Source: The Adventures of Notorious Ph.D., Girl Scholar: Grades in Grad School)
So, this is a story of someone whose advisor told them the cold hard fact of the reality of their grad school life. In the blog post, the author wrote, "a couple of B's aren't going to kill you. But a B can hurt your chances of getting into a Ph.D. program". If a few B's can hurt, imagine what a C can do.
That's why the advisor said, "If you get a C, don't bother asking."
