Hot tubs are known as "petri dishes" by infectious disease experts. It takes sustained temperatures above 130F to kill NTM, so not possible to eradicate in a hot tub.
Here is what was reported by Dr Joe Falkinham, an expert in NTM issues with water:

"NTM cells, as exemplified by M. avium, are collected by air bubbles rising in a water column and upon reaching the surface the bubbles burst resulting in the ejection of water droplets above the water [33,38]. Cells of NTM and other waterborne pathogens, such as Legionella pneumophila and Pseudomonas aeruginosa, can be collected above (1 cm) water surfaces. Further, the density of NTM cells in the ejected droplets is orders of magnitude higher than the density in the bulk suspension" (https://www.mdpi.com/2076-2607/9/11/2262)

I personally avoid the ever-so-inviting hot tub in our winter community.

For years, we had an indoor hot tub in our home, and I have often wondered if it was the beginning of my problems.
Sue

You might wait to get a doctor to order it so your insurance covers it. As I recall the nebulizer is expensive, and the saline is also covered by prescription.