I think that if a Bayonne Bridge line is built, the one way that it will really attract a large number of customers is if it is an extension of PATH, turning south at Grove Street, with a stop at Liberty State Park and either replacing the HBLR, or serving as the express line of it, or both, up to the bridge, then over the bridge, with a transfer station for a potential future North Shore Line, and then perhaps continuing south in the median of the highway to Victory Blvd and in the long term forming a cross-island connection via the SI Mall. The key point, though, is the direct connection to Manhattan, with no transfers.
That would be ideal.  Otherwise why go to Bayonne?  Bleh.

My mom would be happy--she could see her grandchildren without the bus/ferry/subway shuffle.