2017 feels so long ago, but that was when I did a similar trip.
At that time, National Express offered a guaranteed ticket for an extra pound, so if you missed your bus, you didn't have to buy a new ticket. I am glad I did, as I did miss the bus. She wanted to charge me a full new ticket, but I had proof of the extra pound paid.
The drop off in Southampton is a little confusing, as it is very small with just a small multi use kiosk. It actually can be seen on google maps. I see Moxy's is next door to the Premier Inn where I stayed. Moxy was being built when I was there. It is an easy walk from the station.
I was there 2 nights, as December flights from Ontario Canada are best done with buffers for weather mishaps. As it was close to Christmas I did a self guided historical walk, wandered through the Christmas Market (not very big - except the beer tent) and the next day went to the SeaCity Museum. I like Maritime Museums, and this one has both Titanic and Cunard exhibits.
Southampton is small, and rather a backwater these days, so keep expectations realistic.
(also, not sure about which cruiseline you are taking, but I did pick up fresh flowers and wine to brighten my inside cabin. Cunard appears to be rather lenient with that....or was then.