Another 10 day itinerary question

Yikes! Well if you insist anything is doable... :)!

On your present itinerary you could go from London to Bath by train. Trains usually leave around every hour or so- if this is what you plan you'd probably want to get your tickets in advance. The journey lasts around one hour and goes straight in and out of one station (I think Paddington). The Cotswolds are charming -- there are several tour buses and whatnot that go in and out of them from Bath.

Really I'd think about scratching that plan in the first place:

1) Flying into Dublin- and just visiting Dublin. or
2) Flying into Shannon and just visiting Shannon (granted you will have to change planes but its not as bad)
3) From Shannon or Dublin fly to Edinburgh. Visit the city (this takes 3 days)
4) Taking a train from Edinburgh to Bristol Mead to Bath Spa (6 hour journey- 2 changes) (1 day)
5) Visiting Bath and Cotswolds (2 days)
6) London (whatever time you have left).

You really should think about staying longer if at all possible.- or cutting the Ireland section. Its like visiting San Francisco and trying to cram in Arizona and LA in the same trip. Have you thought about scrapping Edinburgh?

Yikes is right!

While most of the trip will be rushed but possible, you cannot see Bath and the Cotswolds in one night. Pick one - if you don't mind a huge detour from the London to Edinburgh route. As you say, one way or another you have to backtrack to splice this into your itinerary - unless you fly from the US into Bristol, which is close to Bath, and start your trip there before going to London.

If your interest is the west coast of Ireland, fly from Edinburgh to Shannon or Knock instead of Dublin. Search for flights on Skyscanner: https://www.skyscanner.com/

Too much whizzing about to places that are far apart! You could spend your entire 10 days doing Bath (with tours to Cotswolds / Stonehenge & Salisbury); then train to York (2 nights); train YRK > Edinburgh. Fly home from Edinburgh or fly to Ireland from Edinburgh.

Also note that you can fly from Dublin to Bristol - which is very near to Bath.

You do not have to go back to London from Bath in order to go by train to Edinburgh. You simply go by train for the 15 minute hop to Bristol (Temple Meads) & then train to Edinburgh / York. See:>https://www.crosscountrytrains.co.uk

Also consider flying from Bristol to Edinburgh.

I would drop Ireland - you are trying to do too much in the time available!

TOO ambitious for 10 days!

I'm exhausted thinking about the time wasted traveling to each of the places you've mentioned and won't get to enjoy.

By train Edinburgh is at least a 4 hour train ride from London.

Public transport to the Cotswolds is virtually non existent. ONLY way to enjoy the villages is to have a car and take your time. It's 2 hours from Heathrow by car. Drove to it last November.

Driving from Dublin to the West Coast of Ireland is a minimum of 4.5 hours. Minimum!

Slow down, sit down and re think how you want to travel in the UK and Ireland. If it's about rushing and not truly experiencing any thing but frustration and when are we going to get there thoughts then stick to your original plan.

Otherwise consider dropping Ireland or Scotland all together.

Or, if you've already committed to flying out of Shannon, then drop Bath and the Cotswolds and Dublin.
Fly directly from Edinburgh to Shannon.

Remember you'll be driving on the opposite of the road which for many can be unnerving so you MUST factor that reality into your speed and distance. You'll also need to travel light luggage wise to ease the comfort of your travel.

Pause. Rewind. Reset.

With only 10 days and 4 destinations ( although Bath & Cotswolds really makes 5 ), the most efficient way to travel, in reverse order, seems to be:
1. Edinburgh to West Coast of Ireland - fly direct to Shannon. The Edinburgh airport is easy to reach and I picked a weekday in May and found 9:00am flights to Shannon with Air Lingus or British Airways which take about 1.5 hours and were priced at well under 100£. Check Expedia
London to Edinburgh - again a random weekday in May shows a train leaving at 7:30 at 25£ which will get you to Edinburgh before 12:00. Trains from Bath to Edinburgh are 3 to 4 times more expensive and take atleast 8 hours with transfers so a non-starter. Check nationalrail website and book asap to get the deals
4 days for London/Bath/ Cotswolds - lots of alternatives but not enough time to see Bath and Cotswolds without really skimping on London.
If Bath and countryside are a priority, I would rent a car at Heathrow, drive to Bath, see the town and spend the night. The next day, drive through the countryside and get a taste of the Cotswolds before dropping off the car at Heathrow and take the tube into London. The negatives are many commentators on this site question the wisdom of driving when possibly jet lagged and you are down to 2 days ( 3 nights ) in London. Bus and train or bus to Bath takes far more time and you will miss the Cotswolds.
An alternative is 4 nights in London, possibly with a day trip to Bath, either day return on the train or a tour. The negative is you will miss seeing Bath and Cotswolds at your own pace but you will not have to worry about driving, shifting hotels and you should get a better feel for London.
While your time is definitely limited, I think it is doable as long as you realize that your trip is more of a sampler than the definitive tour. As always on short trips, the key is to reduce travel time
Enjoy.

Very good suggestions. I'm thinking no to Bath/Cotswolds on this trip or no to Edinburgh
Thank you all