Rail strike in UK

National Express coach service.

The Bath bus station is next to the Bath train station.

On National Express it is a 3 hour journey changing at Bristol, on every odd hour.
Note that Nat Ex don't run between Bath and Bristol, so that part of the journey is on the local city bus service X39 with whom Nat Ex have a partnership agreement.

Note that National Express have doubled their fares on that route on that day.
As you are on the city bus anyway from Bath to Bristol, so have no reserved seat in that section of route the cheaper option is to book National Express from Bristol to Cardiff, and pay your own fare of £2 per person on the Bath to Bristol leg.
There is no dis benefit from that approach, and you had a 1 hour connection at Bristol anyway.

If the trains run that day, then the maximum possible train fare from Bath to Cardiff is £5 less than the coach, from Bristol it is only 1/3 the cost of the coach, on that day.
So the best thing is to wait until early next week when Great Western will publish their timetable for the first of the ASLEF strike days.
That will tell us whether train is viable or not.
If it works on 13 May, then chances are very high on 3 June.
There is no need to panic and rush into a decision. For a short journey like Bath to Cardiff the vast majority of people do not book weeks ahead.
If no train runs on 13 May then book the coach from Bristol, and pay the X39 fare on the day to the driver by cash or contactless.

The Advance Fares between Canterbury and Chester for June 24 were supposed to be posted today, May 3; but I suspect that the rail strikes are preventing this. I think we can get a rail reservation leaving Canterbury on June 23 or even a late bus on June 24 with a very long, 8-hour journey. Should we wait a few more days to see if Avanti offers any fares on June 24 before making a decision?

Sally travels, yes wait a few more days. You'll get there. The planners probably
are busy with two emergency timetables to write.
They are now saying release date tomorrow, 4 May.
You don't want to be getting to Chester at 5.20am, sleepless, as the coach stops every hour through the night, unless unavoidable.
And 2220 is a pretty late night arrival.

LNER don't have the calendar of release dates which Avanti do, so there is no way of knowing.
That's unusual for LNER to be so late issuing.
Kings Cross is closed that day.
You will be bussed from 'somewhere' to St Neots or Peterborough for your train.
Details awaited.

Thanks to isn31c for all the information.

Bath on June 3. We have reservations in Cardiff

TfW Transport for Wales is your friend. They are not striking and their trains will be running.

From their website:

Industrial action

12, 13, 31 May and 3 June

The train drivers’ union ASLEF has announced strike action on Friday 12 May, Wednesday 31 May and Saturday 3 June.

The National Union of Rail, Maritime, and Transport Workers (RMT) has announced strike action at 14 Train Operating Companies (not including TfW) on Saturday 13 May.

Some of our services are likely to be extremely busy as a result of the severely-reduced timetable put in place by other operators.

Transport for Wales (TfW) is not involved in industrial action by members of the train driver’s union ASLEF and members of the National Union of Rail, Maritime, and Transport Workers (RMT).

TfW services will be running but other train operators' services across the whole of Wales, England and Scotland will be limited.

Except that all trains from Bristol to Wales are run by Great Western. To use TfW you would have to get from Bath to Cheltenham on a local citybus.
That was my thought, but was checked on before posting.
The easiest way to get to the ex Cheltenham trains would be the T6 Traws Cymru bus to Chepstow, from Bristol Bus Station, cost £6.50.

It's the same for Glasgow via the West Coast. Scotrail will run from Carlisle to Glasgow, as they are unaffected by strikes, but you can't get to Carlisle as we already know that Northern Rail and Transpennine will not be running North of Preston, and as Avanti are not running on ASLEF strike days there is no route from the South open to Carlisle.
So assuming LNER run, the only way by rail to Glasgow will be via Edinburgh.

Thank you again, Friends in Britain. Patience is a virtue!