Most of those pedestrians on the bridge are motorists. Other motorists and passengers (most of whom are motorists at times) can see the cyclists on the bridge. It means that among motorists, cyclists will have a worse reputation than we deserve.
The absolute worst cyclists on the bridge are motorists who are non-cyclists that rented a bike and have no idea about cycling safety, etiquette, or skills. The lycra riders may startle the pedestrians but in general don't make unsafe moves. The rental riders are completely unpredictable even when they're looking right at you.