in short, bleed works like the old poison mechanic.
Each shot that applies bleed adds to the bleed amount after the resistance has been applied. The bleed amount directly translates into damage over time. The amount of bleed affects the damage per tick as well as the time between ticks.
The cap is 300, at which 30 damage are taken each second. However, since the first tick would decrease the total bleed to 270, the next tick applies less bleed with a longer time between ticks. On top of that, when a target that alread yis bleeding is shot, some amount of bleed is directly applied as damage.
In short, the more bleed you accumulate, the faster you take damage. "Minor bleeding" is easily taken care of by a good healing rate while "profuse bleeding" means more than 200 bleed have been stacked up and should be taken care of quickly with bandages or tourniquets.
The exact formula will be on the wiki in time.