Actually a bit complicated. It was my GI doc who referred me to the bronchiectasis team after me remarking that my PCP suspected my pulmonologist was not being aggressive enough about my cough. I also have Crohn's disease (an autoimmune GI disease) and they share some patients & consult w each other because us Crohnies are more likely to have bronchiectasis. It's not understood why.
There are now several bronchiectasis centers around the country. If you search here or post an inquiry for the best doctors -- include what area of the country you live in -- you'll get help. I'm very grateful for the generosity with good info here.