Q: These little light green bumps surrounded by a black spot showed up on my black eyed Susan‘s almost overnight. They are throughout the patch on many different leaves. Is this a bug or is this a fungus?
A: Widely-knowledgeable University of Georgia plant pathologist, Dr. Jean Williams-Woodward, says you have two things going on. On the lower leaves there is a disease called septoria leaf spot. It can be controlled on new leaves with Daconil (click for sources).
The green bumps on the upper leaves are caused by a sap-sucking insect, the rudbeckia psyllid. Try to control this creature by picking off infected leaves. If more leaves become affected, spray insecticidal soap or neem oil under the leaves.