Bath to Glasgow (and Cotswolds) Transportation

get to Bristol airport then fly to Glasgow with easyjet

Or take a train via Bristol.

Train or coach Bath to Glasgow is a full day.

By train it is 1 change- Bath to Bristol Temple Meads (NOT Bristol parkway) then through train, departing just before 10am or just before noon. Overall it's just over an 8 hour journey.
No matter how you worked out the tickets (you certainly wouldn't want to pay the £143 through fare) the flight is way cheaper and way faster.
Splitting train tickets in a sensible way across Birmingham brings it down to around £63 each. It's too far out to accurately fare but you could normally get that down to around £55, possibly £50, but any lower than £63 involves an added change at Birmingham.
I have just checked the split manually, which is more accurate than the split ticket websites.
Via London is about £64 (advance fare Bath to Paddington, advance fare Kings Cross to Glasgow via Edinburgh) and not much slower but it's the cross city transfer in London. Going from Euston to Glasgow is about £5 cheaper.
Easyjet starts from £25.
The length of journey and the ongoing rail strikes means that Easyjet could be seen as the more reliable option.

Unless you take a hiking tour, I don't know how a tour would help you hike in the Cotswolds. There are one-day van trips from Bath (Mad Max) and from Moreton-in-Marsh (GoCotswolds) that take you to a bunch of small villages in one day. I enjoyed mine, but there was just time to walk around each town for a bit during a brief stop. For hiking, you might explore staying in Moreton-in-Marsh and using buses (generally very infrequent, I'm afraid). I gather that taxis are rare in that area and are often prebooked by locals for things like medical appointments, so this could get tricky. Even if you had a car, I'm not clear on how you'd get back to it at the end of a day's hike.

This topic has come up before. There might be information helpful to you in earlier threads. Try using the Search box, entering hiking Cotswolds.

By the way on National Express you depart Bath at 0824, after changing at Bristol and Birmingham you arrive at Glasgow at 1955. So a nearly 12 hour journey, but no stress about it (unlike going by air).
And at least if the trains go on strike you know you will get there. Book now and you lock in the fare, if a strike is called the fare will double.
That fare is £40 each (or £35.80 if you buy a Bath to Birmingham ticket, then a Birmingham to Glasgow ticket.
However I don't recommend split ticketing. The connection at Birmingham is 75 minutes. On a through ticket if there was a problem on the M5 Nat Ex will hold the 2nd coach, on split tickets they won't so to save £4.20 it's not worth it.
Note that Nat Ex have a through ticketing arrangement with Badgerline, the local bus company, so Bath to Bristol is on the X39- the local limited stop bus. Then you join Nat Ex at Bristol Bus and Coach Station.
Neither Megabus or Flix bus run from Bath, only from Bristol. Megabus is a dodgy 20 minute connection at Manchester.

Thank you all for your suggestions. We'll review everything and go from there.