Bridgeport is on US Highway 395, the main north-south artery along the Eastern Sierra. It lies about 75 miles south of Carson City, Nevada, and about 25 miles north of Lee Vining (the gateway to Tioga Pass and Yosemite's east entrance).
By car is the only practical option. There is no bus or rail service to Bridgeport. The drive from Los Angeles takes about five and a half hours; from San Francisco, about four hours via US-395 coming down from Reno, or slightly longer via Tioga Pass (Hwy 120, which closes in winter).
From Yosemite: if Tioga Pass is open (roughly late May to November), Bridgeport is about an hour's drive from the Yosemite Valley via Hwy 120 East and US-395 — making it a logical first or last overnight stop for an Eastern Sierra road trip.
Nearest airports: Reno-Tahoe International (about 90 miles north) and Mammoth Yosemite Airport (about 60 miles south, with seasonal connections to Los Angeles and San Francisco).