When you take damage that causes bleed but the initial damage only affects temporary HP, do you actually gain the bleed condition when you haven't lost any HP? I ask because injury poison does not work when it causes no damage due to DR, for instance.
Any effect contingent upon hit point loss is triggered by the loss of temporary hit points. Temporary Hit Points says that they are
in addition to the character’s current hit point total and any damage taken by the character is subtracted from these hit points first. Any damage in excess of a character’s temporary hit points is applied to his current hit points as normal. If the effect that grants the temporary hit points ends or is dispelled, any remaining temporary hit points go away. The damage they sustained is not transferred to the character’s current hit points.
…And that's pretty much the entire difference between a creature's hit points and temporary hit points.
There's no rules connection between temporary hit points (that are lost like normal hit points) and damage reduction (that can prevent hit point damage from being dealt, whether as a whole or in part).