The bike route and the sidewalk are one and the same. I walk the sidewalk inbound in the morning and outbound in the afternoon and am passed by plenty of cyclists. It's tight, but there's enough room.
The closed sign on the Ft. Pitt Bridge is leftover from when the park was closed. At that time, the sidewalk ended at a chain link fence right at the Ft. Pitt Museum. Rather than fencing the sidewalk off on the south shore of the river, they put up that warning sign. When they reopened the park (and the sidewalk) in May of 2008 they never removed the sign. You can easily get from station square to the north shore by crossing these two bridges without any detours.