FBinNY 

I've never been on that bridge, but my experience all over the Metro NY area is that you don't get arrested for riding on closed bridge walkways, or even no bicycle lanes. You get a lecture, with a don't ever do that again, or sometimes are sent back the way you came (only once ever).

I don't know if there's a barrier, or how impassible it is, but if you can get access, I'd just take my chances and ride it. If you get stopped, have a sympathetic story ready for why you had to get a cross and that other alternatives are just too far away.

BTW- decades back I rode across the Pulaski Skyway a few times, once a night. On one occasion I drew a police escort who followed me all the way protecting me with his strobes, on another an officer who felt he just couldn't leave me there to get killed (his opinion) and insisted I accept his lift to the other end.

So far, except for a few examples, I've found that cops just want to solve the "problem" and if you're polite will work with you toward that end.

So, if you're willing to risk inconvenience if there's an impassable barrier, you might give it a shot.