I just did Antarctic centre on current coral princess cruise. Took shuttle in (35), walked to transit centre, bought ticket from bus driver (2.10 each way-driver only accepts cash so make sure you have some nz currency, otherwise you need to withdraw from atm) then got off just before airport and walked over the the Antarctic Centre-just after you see the sign for it you get to the stop, so be ready. I bought ticket there but you can buy online and do penguin behind the scenes or different activities. It was a great 3-4 hours, really fascinating and the crew are absolutely lovely to hat with to get more information. 100% recommend, especially the hagglund ride and the storm room, and was a lot cheaper than going through the cruises shore excursion. It took about 30 mins to get out there from Christchurch.
If you wanted to save more, you can catch a local bus from the port for 2.10 and use it to transfer to the airport bus, I found out from experienced cruisers afterwards, but the shuttle was pretty convenient for me.