I tried it myself just now it kept sending me via the ferry by bike but when I switched to walking I was routed across the bridge. I looked at the path and didn't see anything strange. Bikes are access=yes for part of the path and access=designated for the New Jersey side. There's bollard mapped in the path on the New Jersey side but bollard is tagged bike access=yes. Bike access should be changed to either yes or designated for the entire path but I have no idea if this would affect routing. 