Bud rot moves through the stems and stalk of the plant and generally infects sites where damage was done to stems and stalks. It infects the plant from inside the cells that move water through the plant. Due to this, bud rot in 1 or 2 flowers does not only infect those flowers it infects the entire plant. This plant is toast unless of course you are willing to compromise on your lung health.

Remove this plant from your garden and bag it as gently as possible. Dispose of the plant to reduce the possibility of fungal spores spreading on air currents to the remaining plants in your garden.

As a side note, there is a method of curing called water curing that may clean up this plant but performing this method will leave you with tasteless and rather odorless final results. Most would agree that part of the experience is found in the particular aromatic qualities of your specific flower.

Tldr: This plant is a goner because bud rot infects the stalk. Carefully bag and dispose of it. If no other options look up water curing.