There is no practical difference here between the PrPf continuous and the Pr continuous. The PrPf version may be employed to imply a little more strongly that the past month has passed faster than you expected, and the Pr version may be employed to imply a little more strongly that you expect the time to continue passing at the current rate for some time to come; but few speakers are concerned about such very subtle points in such a casual conversation as you describe, where the speakers are unlikely to mean anything in particular.
In a different conversation, of course, the distinction might be more strongly marked:
A: It's been a month now.
B: That long? Doesn't seem like it. I guess time's been going fast.
A: It's been a month. That report is due Monday.
B: Hmm ... You're right. Time's going fast. Guess I'd better get some data.
A: Jeez, Bob, you haven't even got the data yet?!
B: Well, not today's data. He-who-shall-not-be-named will want that folded in before I print the report.
A: You mean you've already written it?
B: Al, time's been going fast—but not as fast as me.