A bridge assembly is disclosed for use with an internal combustion engine. The bridge assembly may have a valve bridge, a cylindrical housing disposed within the valve bridge, and a plunger disposed in the cylindrical housing and protruding from the valve bridge. The bridge assembly may also have a valve housing, a post located inside the valve housing, a plurality of obliquely angled ports passing through a straight annular wall portion of the valve housing, and a plurality of radially oriented ports passing through a tapered annular wall portion of the housing. The bridge assembly may further have a valve seat disposed at least partially inside the plunger, a ball disposed within the valve housing and movable between a distal end of the post and the valve seat, a first spring disposed over the post, and a second spring disposed within the cylindrical housing.