DH received a bridge tour on the Fantasy on June 7th 2013. They only do it while in port and no issues with weather and such.
To get an invitation you must go to the Guest Services desk and request to send a note to the Captains Assistant. They should give you a card and envelope. Simply address the note to the Captain and make a note that if at all possible you would like to have a tour of the bridge. There is no guarantee that you will receive an invitation. Give it a try.
The tour DH went on was while the Fantasy was at
Castaway Cay. This was after the Fantasy had made an emergency stop at Nassau before going to Castaway Cay. We only had about 5 hours at CC so I think that may be the reason they were giving tours that day.
DH did say that others were on the bridge while he was there an others coming in. Do dress nicely, he said. You don't need full dinner attire, however; no tank tops or wet swim suites. Just clean up a bit. The bridge is a special place so be respectfully dressed and mindful of the crews time while there. DH was impressed with how posh the bridge seems to be. VERY orderly as well, he said. DH was on the USS Eisenhower so this was a major step up in quality, he said.
HO!!... We are gold
Castaway Club Members to that may have helped.