The bridge network was an expansive implementation of a worldwide series of Einstein-Rosen bridges by the United States government. It was designed to be an extremely quick and efficient public transportation system.
It suffered a setback during development when Rudyard Shelton grew disillusioned with the project and abandoned it to go live in an unknown location, leaving behind only his notes on the temporal mechanics aspect. The government enlisted Oscar Shelton to take Rudyard's place, but he proved unable to fill the role and quit. Despite this, James Zanasiu and Yuri Kerzach managed to complete the work. (Ask the Characters)
It opened in 2033, and was met with wide public approval and acclaim. Unbeknownst to almost everyone, it was also afflicting everyone who traveled through it with Shelton's disease, though the impending epidemic was cured through the efforts of Dr. James Zanasiu and allies. ("CS:Pilot")
Malte Kerzach mentioned "catching a bridge to Washington DC" in 2053, implying the network was still active and functional. ("CS:The Meaning of Love")
At some point, the traveller appeared in New Pelvanida through one of the networked bridges, though the connection was anything but local. (Find the Cure!)