I think you need to rent a car.
There might be ways to work the systems of busses... but not all that easily.
From the website:
Taxi is a possibility, as there are shuttles to almost everything, once the mountain is fully open, but were I flying in, I woudl certainly rent a car.The convenience of flying into Vermont's Burlington International Airport is unparalleled. You can land in Burlington and drive to Sugarbush in just 45 minutes. Taxi, group transfer service and car rentals are available from the airport. Rates available upon request.
The following airlines provide service to Burlington:
Hope this helps.
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