Looks like the only fare they have listed on their page (https://civitavecchia.portmobility.it/en/shuttles) is the "Direct Cruise / Railway Service" for €6 that's been mentioned several times here. So I'm fairly confident both the green line and blue line are free, but of course it seems like there's a lot of moving pieces and the info seems to be changing all the time, so we'll see what happens.
Also, I noticed going further down that page that they have a map with the various stops -- looks like the Molo del Bicchiere stop is on the other side of the fort from the Google Maps location I'd previously noted:
If you look at the area in Google Maps, there's a pin with a location marked "Royal Caribbean bus pickup" that looks like it's in this location:
We'll be departing on June 12, on RCL Enchantment of the Seas. It'll be our first cruise, so there's a little trepidation, but our boys (ages 10 and 8 ) are already fairly seasoned travelers (we've taken them to Europe three times, Costa Rica, Puerto Rico, and all over the US), which definitely helps lessen the anxiety about catching all the various trains, buses, etc.
Mostly, I'm just a planner and like to know all the details ahead of time and exactly where to go, backup options, etc. 😉