Train to York

The train from Bath to York was covered pretty thoroughly a little while back in another thread: https://www.ricksteves.com/graffiti/helpline/index.cfm/rurl/topic/100108/train-from-bath-to-york.html Bottom line is that it's faster, more scenic and direct to Bath (Spa) to Bristol Temple Meads and then change for York rather then go via London. And probably cheaper if booked here: http://www.farefinder.crosscountrytrains.co.uk rather than the official site: http://www.nationalrail.co.uk That leaves your question about the Cotswold area but it should answer your Bath question pretty well. Good luck,
=Tod

The Crosscountry Trains service from Bristol Temple Meads also stops at Cheltenham Spa, which is the closest station to the Cotswolds area on that line.