Train Bath to Conwy - May 2023

You can do it in under five hours with only one change, at Newport. Then up through the Welsh Marches (Shropshire, Herefordshire).

You don’t have to arrive late if you set off early.

A random Sunday in May gives a departure at 12.28 with one change. Arrives around 17.30. Cheaper tickets probably not on sale yet. Look out for possible engineering works on a Sunday.

There are several ways to do it, but yes the Newport route is the most logical and it'll take you 5 hours.
If you leave Bath at 1228 or 1430 it is only one change at Newport. The Newport to Conwy train is going to Holyhead.
So sit back at Newport and enjoy.
Other trains are 2 changes.
You should pick that up for £30.50 each. Interestingly the through advance fare from Bath is cheaper than split ticketing on Newport, as the fare from Newport to Conwy is £3 more than that from Bath!! A system quirk.
It's something like a 200 mile journey through picturesque scenery so 5 hours is not bad going.
Be aware that the first and last Sundays of May are Bank Holiday weekends so will be busier and are more likely to mean rail engineering work.
On 7 May there is a warning on the journey planners of bus replacement in North Wales between Rhyl and Llandudno Junction- times to be confirmed on 13 March, so you have at least 4 weeks to wait yet before you can book and confirmed times are available.
It doesn't seem that Transport for Wales have opened advance tickets or confirmed timings yet so only the dearer £57 fare is being offered currently.
The National timetable change is on Sunday 21 May.

Our date is May 21 and what happens to the schedule on May 21? It switches to summer schedule? Is that better or a concern?

It is the change to summer schedule.
There are not normally extra trains added on to either of these routes for summer,
It's just a note because until both GWR and TfW confirm their summer timetables, you can't book unless you are prepared for later amendments. It's a date when booking schedules are often compressed, like the winter change in December.
There is no talk of huge changes being planned on either route so not a big concern.
PS- Conwy is a tourist town so if you book ahead (others will have restaurant recommendations for Conwy) dining will not be a problem.

I’m seeing £114.00 2 people from Bath via Newport and then to Conwy - only 1 change. Arrive at 17:30ish. Seems to me if I miss that train or there is a connection problem, I’ll be in trouble :(.

Is that cost right? And how do I buy an advance fair? We are both over 60 and I haven’t looked into rail pass yet.

Also - is there a problem getting seats - do they sell out?

If you put in a Sunday date in mid March you'll see the £30.50 each fare.
If the 1228 from Bath was late into Newport (or was cancelled) your ticket is automatically valid on the next train (a bit under 2 hours later from Newport), likewise if the Newport to Conwy train was cancelled you just take that next train.

You don't have to do anything if that happens.
It's a 16 minute connection at Newport- so you've got plenty of time to switch platforms. There are elevators to go up and over the bridge between platforms. If it's looking tight ask the train manager on the train from Bath to ring ahead, and they may even hold the other train, as you won't be the only one making that connection, especially given the 2 hour wait.
You'll still be into Conwy before 8pm.

If you were that late the delay repay system would give you a 100% refund so the journey would be free!

All the train managers have I Pads so can easily check that your connection was missed through the national train running data if they ask. In truth most of them aren't going to bother if you're on a later train.
Just buy tickets from either the Great Western or the Transport for Wales website.
As there are two of you, if you do the Railcard thing, buy a Two Together Railcard- one card for the two of you at £30, rather than a Senior Railcard at £30 each. It can be bought digitally before you arrive. On this journey alone that saves the two of you a combined £20.40. If you're doing another journey like London to Bath or Conwy to London/where-ever you are into savings.

In reading everyone’s information (thank you!!) a thought just occurred to me.

Is it easier / better to take the train from Bath Spa to Llandudno Junction on a May 21st and then take a quick taxi ride to Conway? Wondering if that could get me in earlier?

Not really, it's exactly the same trains to Llandudno Junction as to Conwy. Conwy station is in the heart of the town, and it's only a 6 minute train ride, if that, LJ to Conwy.
The only benefit is that, although everywhere in Conwy is walkable from the station, there are no taxis at the station, so a taxi from the junction would take you straight to the hotel without the (short) walk.
Horses for courses.
You can always book to Conwy (same fare) and get off at the junction if you are feeling like that when you get there. No-one will know or care. There's a rank outside, so no need to book one.
Maybe call the hotel and check how close they are to Conwy station.