I think it all boils down to narrative conventions, actually. If you go faster, time does not slow down, even relative to you. You're just going really fast, period. Maybe something biologically can happen so EVERYTHING seems to slow down, including yourself from this high speed to a "normal" one. But relatively, there's no time frame change until you hit the point where yes, a noticeable relativity effect comes into play, and you go slightly slower relative to the "outside world."