You don't quote the location in South Wales, but you can type in the town & if there's no service from there the website will prompt you with a map of the nearest stops. (if you're struggling, post again with you S. Wales location & one of us will figure it for you)
Your destination is Southampton (coach station).
Don't select the "cruise ship terminal" option
, it doesn't apply to your ship & you'll get a "no service available" message. Or worse, you'll be taken to the wrong cruise terminal
Pre-booking is very very strongly advised.
And do check the website's terms re luggage. The limitations are usually applied only very loosely, but if you grossly exceed it could be a problem if the coach books out & other folk have a lot of luggage. Since this isn't an airport run, it's unlikely to be a problem, but do be aware.
Coaches aren't that frequent, & most south Wales to Southampton journeys are routed via a change in London. That's quite a roundabout route so a journey time of six or seven hours. Fare around £25 to £30
You'd almost-certainly be better to travel by train
There are frequent trains, including hourly direct services with journey times of about 2.5 hours (though you might have to start with a local train) and depending on your start point & time it can be cheaper than by coach. For example 09.30 from Cardiff arrives Southampton 12.04, fare £18.
Your destination is Southampton Central.
No need to pre-book though that might give you a small saving, and no luggage limitations/cost.
Post here again if your travel is on a sunday, there are a couple of caveats
From either Southampton coach station or train station to any cruise terminal is a taxi hop costing about £6 to £8, taxis are ranked-up at both