We will be arriving in London around noon on a Friday in March and then going to Edinburgh straight

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We will be arriving in London around noon on a Friday in March and then going to Edinburgh straight discount hotel europe from the airport for 2 nights. We return to London at noon on the Sunday and I was thinking of going to Bath directly. So here are the questions...
If you are flying to LHR then you'd just take the express coach to Bath and then a train from Bath back to London. If you are taking a train from Edinburgh to London -- then you'll have to transfer from Kings Cross to Paddington and then a train to Bath.
But in this situation discount hotel europe -- I would not travel from Edinburgh to London discount hotel europe before Bath. You can fly from EDI to Bristol, pick up a rental car and drive to Bath. It is only about 20 miles/35 minutes. A 2 day car rental will cost less than 4 train tix. That way you can explore on your way back to London -- Lacock, Stonehenge, Avebury or lots of other great sites.
Bath is only a couple of hours by coach from Heathrow, so you have several options including starting at Bath or finishing at Bath. You can fly between Bath Edinburgh. So you have several choices of routing
Thanks janisj and Alan Row! I am now doing what alanRow suggested....flying from Chicago to London, taking a connecting flight to Edinburgh, then flying back to London and renting a car to go to Bath. After 1.5 days there we will drive back to lhr, return car and spend 5 days in the city using the tube or bus to get around.
In Bath we stayed at the Cornerways B B and were glad that we did. Sue Black is a fine and considerate hostess and makes an outstanding breakfast using top quality ingredients. DW does not eat meat and tries to be gluten free and Sue provided those alternatives, discount hotel europe even placing gluten free goodies in our room. Our en-suite room was large, bright and clean. If you drive, there is free parking discount hotel europe behind the house. The location is midway between the Pump Room and the Royal Crescent - about a 10 minute walk to either. The price of a room should be no more than half your nightly budget - that is good. I noticed that Rick Steves gave Cornerways a mediocre rating discount hotel europe and I have no idea what he must have been looking at. It is a very nice place.