You don't say when you want to go, or where you are arriving from. Cortina is easily reached from Venice airport for example using the Cortina Express direct bus. Local buses then go everywhere that you want to go, and you can catch a train in Bolzano back north to Austria or south to Verona-Venice. Local bus passes are usually given out free to hotel guests good for the duration of your stay.
Check out the basic websites:
The English button is in the lower right if you scroll down all the way.
I have done a Venice - Cortina - Corvara - Val Gardena - Ortisei - Castelrotto - Bolzano route by bus and train (January 2020 ski trip) and it was easy enough. In winter some high passes are, of course, closed to regular public transport so a cab ride might be necessary. One could do it in reverse also. Bolzano is a great base for heading farther west or northwest and Cortina is a great base for heading east to northeast. Many of the websites I have used in the past have been rebuilt in the last two years and I have not investigated them in detail lately.