This short line ran between its namesake towns, from a mainline connection at Bath to Hammondsport, on the south end of Keuka Lake. The mainline connection was with Conrail (formerly the Erie Lackawanna and the Erie Railroad before that).
At some point in the 1990s, the original shortline segment was placed out-of-service. The rails are still intact; however, the right-of-way is choked with weeds for much of its length.
Interestingly, the B&H is still active elsewhere, as it now operates the former CR/EL/DL&W mainline it connected with! (The B&H operates the line between Wayland and Corning.)
Thanks to Mike Palmer for contributing information about this route.