Cardiff Hop On Hop Off Bus

https://www.hop-on-hop-off-bus-tours.com/tour-city-sightseeing-cardiff-hop-on-hop-off-bus-tour
is the one that seems to exist.

However, note that many attractions are all within walking distance of the Central station such as the Castle and National Museum of Wales. The Bay (waterfront) is just over a mile mile south of the main shopping area but I suggest that you use the Cardiff Bus number 6 which goes about every 10 minutes from a stop on the south side of the library across the street from the entrance to the Marriott Hotel.

Also note that 3 other castles are found within about 7 miles of central Cardiff. You can read about these in my response to another
query:>https://community.ricksteves.com/travel-forum/england/trip-planning-d8d2d7b7-5735-4a38-9c1e-d3bc02c3d61e

For St.Fagans Castle & Museum, you need Cardiff Bus 32 (Hourly - not Sundays). This service will start in April 2024. See >https://www.cardiffbus.com/services/CB/32

Cycling tours >https://ding.wales

However the above website seems to be a third party website.

The City Sightseeing website (their own site) does not reference a Cardiff service. Whether this is because it has not yet started its season or it is cancelled this year is not at all clear.

It appears that City Sightseeing is a franchise model business that uses local operators under the brand. Cardiff is not listed so perhaps whoever actually operates the Cardiff service does not wish to pay then a cut. I would just rock up in Cardiff and pay direct to the bus operator should you actually happen to see such a bus when in Cardiff. As I said earlier, it is quite easy to see everything of interest in the central area and bay on your own.

The website I quoted earlier does indeed appear to be a third party booking site so best avoided.

by following the (hard to locate) crumbs on the official Visit Cardiff page, I have found that TooTbus run an open top bus.

With 14 stops along our route, you will have breath-taking views of
Cardiff Castle. Principality Stadium, Norwegian Church and Cardiff Bay
– all from 4 metres high. Tune in to our entertaining and informative
audio commentary on board the bus available in 7 languages- English,
Welsh, French, Spanish, German, Italian and Polish and discover all
that Cardiff has to offer. Download the Tootbus app to locate our bus
stops, explore the city like a local, and track you bus in real time.

Tours operate all year round, every 30 minutes (no service Christmas
Day, Boxing Day and New Years Day). Tickets are valid for 2
consecutive days allowing you to hop on and off the bus as many times
as you wish during this period.

So sit back, relax, and let Cardiff simply take you by surprise!

TooTbus generally operates off the app. The same company as in several continental Europe cities, and is owned by RATP, the company which runs the Paris Métro and buses.

so, continuing down the rabbit hole letting google point the way, I find that TooT are only operating in Bath, London, Paris and Brussels.

They no longer appear to be operating in Cardiff or most other places.

Good luck...