Conwy to Llangollen by public transit

Is this for a canal boat tour on the Shropshire Union Canal?

It is the Pontcysyllte Aqueduct tour

There is an oddity on Traveline Wales that it is not giving a through journey, maybe because one of the connections is wholly in England. If you plot the journey in two halves on Traveline Wales it gives it (Conwy/Llandudno to Chester) and Wrexham to Llangollen.
If you ask Traveline Wales for Chester to Llangollen it gives some journeys as being fastest on the T3 changing at Ruabon- the Traws Cymru Barmouth to Wrexham bus (as there the bus stops at the Station, rather than the walk at Wrexham between Rail and Bus Station).

Here is the T3 schedule. You can get a train to Ruabon and get the T3 bus to Llangollen Parade St. Walk across the bridge over the Dee and the Llangollen Warf is straight ahead above you. You'll have to walk to the right, then a left at Warf Hill Rd.
https://lloydscoaches.com/t3-trawscymru-barmouth-dolgellau-bala-wrexham/

You could, if you wished, not go to Llangollen but just catch a train from Conwy to Ruabon and then the T3 bus. Tell the driver that you want to see the aqueduct and that you would like to get off at Trevor - which is about 15 minute walk from the aqueduct. If you go on Google maps and put in for Ruabon and then Trevor, you will see what I mean. The bus stops are clearly marked in blue - remember that we drive on the left so one side of the road will be westbound and the other side eastbound. Of course, you could just go through to Llangollen and take the canal ride - as was your original intention - I am just saying that the bus passes near to the aqueduct.

Check your train times and that they match up with the T3 buses at Ruabon.https://www.nationalrail.co.uk

PS. If you have time on the return - take a walk around Chester.

Thanks everyone! Interestingly enough the transport for Wales site and others do not mention a T3 bus only Arriva buses and line #5. I am copying the info from the forum and taking it with us. We have a ticket by train to Wrexham because it was the only bus line I could find to Llangollen online at the time. Ah well.

There is no reason why you can't purchase an add on train ticket from Wrexham the one stop on to Ruabon, on the day.
I wrote having done a computer check, and knowing that the T3 is the 'usual' recommended rail connected route to Llangollen.
I have just done a manual check, and the next station beyond Ruabon is called Chirk.- so 2 stations past Wrexham.
There is also a rather irregular bus, the 64, to Llangollen from there. If your return timings were right that is another possibility- don't wait around for it, or go out of your way. But it's a different route. For the sake of completeness and as reference to others
https://www.tanat.co.uk/images/64_timetable.pdf
The Llangollen Canal, further in it's journey, goes through Chirk, and there is a fine Castle there as well, for another day!
If you had your own hire boat on the Canal that is one of the stops you would make.

A day return train ticket from Wrexham to Ruabon is £4 or £2.60 with a railcard, or to Chirk is £5.80/£3.80

what I would have done back in the day and it should still be possible with a half way competent Guard / Conductor / Senior Conductor / Train Manager (synonyms) - I would "Excess Over Distance" the ticket which would only add the cost of the difference in the original fare and the new longer one. It is even possible to Excess the ticket for zero pence if the fares are the same fare base and identical. The calculation is done by the ticket machine these days (not the public one, either at a booking office window or with the said Guard) so you know it will be right (LOL)

I'm not sure how that would work on Northern where all stations are now Penalty Fare Stations. You either have to have a ticket for your full journey, or a promise to pay notice before you board a train.
Almost all stations now have ticket machines.
No excuses.
If the machine is easy the official rule is that you must purchase on line.
If you haven't and TTI's are around it is an automatic £100 penalty fare.
Where I live almost all stations are unstaffed so there is no ticket office to visit to get an excess fare.

We bought tickets for the train in advance, but thank you for the warning and to others using the trains. Next time I swear I’ll buy a pass because that is way easier than a lot of point to point tickets. We didn’t this time because our train estimates were low. As it turns out we’re on trains more they we thought originally. If a pass is within $150 I’d do the pass. That was blissfully simple.

It is possible to purchase Rover tickets in Britain. Unfortunately, the new National Rail Website does not include maps of the lines on which these are valid - which could be confusing to foreigners not familiar with place names.
https://www.nationalrail.co.uk/ticket-types/promotions/?promotionType=ranger-rover

The North Wales Day Ranger All Zones at £38, or £25 with a railcard, which includes almost all bus routes, may well have been the better ticket for this journey, with hindsight.
At least in terms of flexibility.
One to file away for others to be aware of.