Bulk guy is specifically referring to the pitcher who comes in after the opener. This term didn't exist before the Rays invented openers a few years ago. They are starters who aren't very good.
Long man is the guy who comes in when the starter gets knocked out early. This is not planned, and they could be expected to cover 4+ innings. They are often also spot starters/swing man/6th starters. However some teams will keep a 6th starter stretched out in AAA. Long man can be a guy who's just not good enough to be a starter, like Paul Spoljaric, or a young starter who needs big league experience like Halladay and Hentgen.
Mop up guy is slightly different from a long man, because they're not necessarily there for long outings. They are there to soak up 1 or 2 low leverage innings at a time to rest the better relievers. They'll come in for the 9th inning of a blowout, for example. Mop up guys are almost never top prospects unless they are rule 5 picks. Trent Thornton is kind of filling the mop up role this year.