I haven't tried it myself but the Flesh Stick bug is supposedly a good way to level (I'm a bit lazy so if you're interested you can google it up). If you want to level quickly legitimately, here are the quests you should avoid if you want max-level unique rewards: http://orcz.com/Borderlands_2:_Unique_Mission_Rewards?quests=unique
Honestly, I feel like if you're going to want to level using the Flesh Stick bug, you might as well cut out the middleman and just look for a save editor to edit your level to 50...
I've found Bunker faming to be really fast. Sadly, I did this to make a few bank alts and it's nice between the exp and all the eridium he dumps out. You just need one friend to make a PT1 game and don't join until they're at the bunkers area. Once you get up to 30 or so, have one of them run you through the story so you can get into TVH mode, do more Bunker runs (ideally, one of them will be zero to make them especially fast) until you're 40-43 and then go work on the story or keep blowing up bunker until you have decent enough equipment to work on warrior or whatever you want.
I don't think you have to beat the game on normal to join someone elses PT2. I leveled my brothers level 1 siren (7 by the time I got there) to 35 or so on TVHM flesh stick.
Btw, in case you wonder what the fleshstick glitch is. In the sidequest you can get from Tiny Tina you will at one part "invite" flesh stick to her teaparty. If you kill him he gives xp as if he was a boss, yet he easilly dies with one shot. Thus you have one person back at Tiny Tina to accept the quest, another stands where he spawns and kills him, the quest fails and the one back at Tiny Tina accepts the quests again, spawning flesh stick. Rinse and repeat untill game bugs out (happens once in a while). Then you can just quit the game, reload and do it again. That would probably be the fastest way to level if you have at least one friend at that quest.
"homer the lord only asks for one hour a week" -Marge "in that case he should have made the week an hour longer..." -Homer (GF)