Had a big bump above my clitoris not painful or itchy, during a warm bath it popped with pus and blood, what is it?

A cyst. This was likely a cyst. They can be common in the genital area. As long as there is no pain, or fever, you can feel safe that it has now gone away and no further action needed. If it comes back or becomes painful, you should see your local doctor.
Skin. It may have been a type of pimple or small cyst. One of the things we recommend to patients with either of these things is to soak it in warm water or with warm compresses to help it dreain and heal and so the fact that it popped when you were taking a warm bath makes perfect sense and confirms that this is likely what it was. Going forth, you could put some antibiotic ointment on it until healed.