The Helena Airport (HLN) is less than ten minutes from downtown Helena. Uber, Lyft, and Taxi are all available from the airport as well as rental cars on site.
The Bozeman Airport (BZN) is a beautiful 1.5 hour drive from Helena. If you take I-90 to US-287 you'll drive through literal "amber waves of grain" and see wide open views of the Bridger, Tobacco Root, Elkhorn, and Big Belt Mountains. You will also cross the Missouri River several times, following part of the Lewis & Clark route.
From the East: Take I-90 to exit 274 and head North on US-287. This will lead you directly to Helena.
From the West: Take I-90 to exit 174 and head East on US-12. This will lead you directly to Helena.
From the North or South: Take I-15 to exit 193 and turn West on Cedar