It is worth playing around as often, but not always, the next train (1228 out of bath, 1737 Conwy, 17 minute connection at Newport) is a cheaper train.
Times and fares for the same train on the same day should always be identical on any train company website.
Put in Bath to Newport into the planners, see what fares you get, then try Newport to Conwy, then try Bath to Conwy.
If you wanted to take the earlier train but wanted more time at Newport on split tickets you would take the 0911 from Bath. On the early train both the 0911 and 0940 from bath are changes at Bristol Temple Meads before Newport.
On the 1228 the train goes straight to Newport, so one less chance for things to go wrong at.
The 12 week rule on Advance Tickets varies between companies. In this case you are too soon (!), not too late. T(ransport) f(for) W(ales) rarely reaches the 12 weeks. On many companies you can set up a notification for Advance fares release- I can't find that on TfW.
Although not super cheap you can get "advance" fares in Wales up to 5 minutes before travel.
You can't do it on the internet but on the ticket machines at my local station, when I book an advance ticket I can specify the length of connection I want.
If you do miss the connection you are automatically accepted on the next train 2 hours later.
Normally at Newport you cross a bridge inside the station to switch trains, but sometimes it is a cross platform connection- just depends.
Although I don't recommend it, in my part of the country I often see advance fares go down about a week or two before travel. It's a case of judging the sweet point. Two fares on Bath to Conwy at £60 is as good as it gets. If you find those bag them quickly.