iNano78 is correct.
Bleed doesn't work because plants have no blood, so they can't bleed. However, Bloodthirsty and Vampirism don't depend on blood despite what their names may lead you to believe. They make more of a statement about the attacker than the defender.
Bloodthirsty can easily be explained without any need for blood. It's simply an overly aggressive creature that goes berserk when they sense an injured foe. Vampirism is a little more difficult because it kind of requires you to change your normal concept of a blood sucker into something more mystical that feeds on their life force.
Regardless of your individual thematic interpretation though, the answer to your question mechanically is that they both work on Plants and any other Living Creature regardless of blood. This is because, like iNano78 said, they are listed in the rules as working on all Living Creatures without any stated exceptions.