In Small to Medium sized cities in the US we usually have private company run airport shuttles. We also have some ethnic community with their own "China Town / Saigon Buses" going point to point without airport involved.
Then we have people asking friends and families for rides, "Limo" companies, rental cars, etc. The worst case scenario of people getting stuck is real, but the typical regular demand for a regularly scheduled services is not there for Greyhound.
As a comparison, Greyhound would take 11 hours between San Jose to Santa Ana in California. The Vietnamese bus typically takes 7, and is cheaper. The only thing you have to tolerate is the Karaoke MTV onboard.
For shorter distance like within San Francisco Bay Area we have local buses for commuters, like SamTrans, AC Transits, VTA, etc etc. It is for commuters, not airporters. We also have those TechBus that big companies run for their employees.