Upgrade bid and taxes

I am thinking about making an upgrade bid from PE to UC for our JFK - LHR flight in September but am wondering if the bid price (if successful) would include the taxes or not. Is trying the FC No. and just asking a cash price without bidding worth a go.

Thanks Michael

Your best price will be when you arrive at JFK for your return flight.
Have upgraded this way a few times and always got a good deal.

Never tried the upgrade bid process.