I never road it but the Greensboro bus system seems to be expanding to all Triad cities.
So to answer your question yes there is a bus from Greensboro to High Point and Winston-Salem.
In google, you can type 'bus service from (city of you choice) to (city of your choice). To me, it appears to provide service during peak hours.
I notice PART provides an app to track the bus location.
Piedmont Authority for Regional Transportation | It also has info on ride sharing too.
I saw commercial of another service that provides shuttles from Greensboro airport to Charlotte airport but cant find it name at the moment.