As an operative I have Bleeding Shot and make level bleeding damage if I hit.
My question: what happens if I do bleeding damage after I hit the first shot. Does the bleeding damage stack?
Unfortunately, there is some ambiguity in the rules about bleeding.
While the description of Bleeding Shot speaks about bleed damage, the description of Bleeding Condition uses the terms bleed effect or just bleeding.
If we assume that both speak about the same thing, which is very likely, then the answer to your question is here:
You take the listed amount of damage at the beginning of your turn each round until this condition ends. Your bleeding can be stopped with a successful DC 15 Medicine check as a standard action, or through the application of any ability that restores Hit Points. If you take two or more bleed effects, you take only the damage from the worst effect.
I.e. bleed damage doesn't stack, only the worst bleed effect on the target applies.