Wow that was vague I was tired. As in, passing someone on the road, or in a competition, what?
On the road it would be עוקפת. At least if you mean that both of them are going on the road, and the speaker takes over the man.
You can say "אני עוברת את החנות", meaning "I go past the shop". I guess you can also do it with a man, but it sounds funny, as if the man is some landmark...
Context where I'd expect עוברת את הגבר are maybe in grades, height, something like that.
I'm pretty sure עבר is only "to pass by," as in הוא עובר אותה כל יום, or "He passes by her every day."
What's the difference between עובר sth. and עובר ב sth.? Another exercise goes like this: כשאתה עובר במכולת...