Getting out might be possible by fat-tire bike, but roving gangs would have to be avoided and they will be out in force as soon as they see all that unarmed loot backed up on the freeways and bridges.
And with the Police overloaded, ferals in Manhattan will start to loot apartments and stores.
That said, the best route to safety is over the GW Bridge by mountain bike. Once on the other side, enter the Palisades Park on the north side and walk your bike through the wood to the switchback foot path down the Palisades exactly .45 miles NNE of the GW and make your way down to Henry Hudson Dr (which is protected by the cliff face of the Palisades and the ferals will be busy with the heavy loot areas). And then head north on the HH Dr to suburban safety.
GW Bridge? You mean past it, not over it (which will deposit you in NJ)?