The Bridge lines opened in 1917. New Haven Steam operated over **** Gate from 1917 to 1918 for passenger trains and from 1917 to 1927 for freight trains . The lines were electrified as follows.
1918 Two passenger tracks 1 and 2 to Harold at Sunnyside. New Haven Electric Power changed to PRR DD-1 for trip into Pennsylvania Station. This operation lasted into the 1930's until the PRR installed catenary through Pennsylvania Station. New Haven Electrics then operated into Pennsylvania Station.
1927. Two Freight Tracks 3and4 to Fresh Pond and then to Bayridge. New Haven Steam, generally Mikados handled New Haven Freight from Oak Point to Bay Ridge. In 1927 the catenary was installed and New Haven Electrics handled the work replacing New Haven Steam for regular motive power. LIRR Trains on the Bay Ridge Branch were steam powered usually H 10s, into the 1950s. Largest power used by the LIRR were some L class Mikados leased from the PRR during the war years .
I believe the General reproduction may have operated over the Bridge under steam in the 1960s.