You have to do the armor quest that takes you to the university. Finish that quest line and the professor will give you the recipe for the enhance bucket.
I did that, was sent to mine some black iron ore, but never got the recipe. I can't do anything with it without the mithrill bucket, because I need lava.
Just to clarify you gave the professor yellow essence from the Raijuu correct? Cause after I did, I was given the recipe. I believe it was for the Anti-Cold Armor.
