No, I can assure you that bronchiectasis is not contagious. In my case, it is probably a genetic predisposition compounded by lifelong asthma and repeated bouts of pneumonia as well as repeated exposure to industrial paper dust and asbestos. My daughter also has the same set of issues and so did my Mom, who also was exposed to paper dust for 40 years. My husband's case is quite different, and is a side effect of the specific type of rheumatoid arthritis he has. It looks very different on his CT than mine.
Incidentally, my Mom had bronchiectasis for years, and died in her mid-80's of a completely unrelated cause.
The types of lung infections we often get are likewise not contagious. With our compromised lungs, we are more likely to catch respiratory bugs from others, so I am especially careful.
Sue