Car Rental

That price is right in line with what you would expect to pay for economy so that's fine...there may be other fees that can kick up the cost a bit but it looks good to me. The price is low because it's a manual transmission.
Renting a car in Europe is fairly straightforward. No different really than renting a car in your home country. Just make sure to sort your auto insurance and/or check with your credit card company that you are using to pay to see what kind of coverage they include if any.
My biggest thought for you would be about your comfort level with driving on the "other side" of the road (I'm assuming you live in a country which drives on the right??). This, in combination with the fact that you plan to rent a manual transmission car, may be something to seriously consider. Remember, not only are you driving on the left side of the road, you are also sitting on the right hand side of the car, with the gear shifter to your left. Everything will be the opposite of what you're used to. I've driven quite a few cars in England on numerous trips and believe me please when I say it's not as easy as you think it's going to be. You'll get used to it but just be prepared for a steep learning curve. Don't pick up the car in a congested urban area...pick it up outside of town in a smaller place so that you can practice before you get going on your trip. Even Bath can be challenging to drive in...Edinburgh - no thank you!
My other thought would be about your itinerary. If you are planning on touring cities then renting a car is not at all practical. European cities are difficult to drive and park in and it can be very frustrating and time consuming! Train travel is usually recommended if cities are your primary destinations.
That all said though...renting a car to drive outside of Edinburgh, out into the more rural areas, is a great idea. That part of the world is best seen by car IMHO.

Anita offers sound advice. If you are renting a car in Bath just to drive up to Edinburgh, you would be better off going by train or flying from nearby Bristol. www.skyscanner.net

For trains - www.nationalrail.co.uk - you will need to purchase an Advance one way fare from BTH to EDB via CNM (Cheltenham). (Fares appear on the system about 11 weeks ahead - and that is when they are cheapest. However, even pre purchasing specific trains a day ahead is far cheaper than walk on fares for most routes.

Car rental would be useful for driving from Edinburgh to the Scottish highlands. (I would head for Pitlochry and points west but a joinery to the Isle of Skye, for example is no quick day trip from Edinburgh).

When returning by train from Edinburgh to London (Kings Cross), you might like to consider an overnight in York and then, with a separate ticket, resume your journey to London the following day.http://www.visityork.org

If you are just going Bath straight to Edinburgh I would suggest taking the train from Bristol Temple Meads. You haven't factored in the price of fuel which will make you weep and having a car in Bath or Edinburgh is pointless. The Cross Country Trains service goes via York on the way up so you could stop off there ( or on the way back to King's Cross - the Virgin west coast service goes via York heading south).

or on the way back to King's Cross - the Virgin west coast service goes via York heading south

That would be Virgin East Coast, as I am sure was meant by melsmith1962.

Virgin West Coast (unable to operate at the moment from Scotland due to the flooding) is via Carlisle, the Lake District and Birmingham.

Thanks for all the great advice! I may consider fore-going the savings on a manual and rent an automatic after all ;)

We were thinking a car would make sense as we'd like to use it to see the sights around Bath (Stonehenge and Avebury, as well as a drive out to Cheddar Gorge), and then drive through the Cotswolds (staying a night or two to explore the area - Chipping Campden/Stow-on-the-wold), up to Derbyshire (want to visit Chatsworth Estate), a night over in York (a business meeting there), and then thought that it would be easiest to drive from York to Edinburgh so as to be able to visit Hadrian's Wall. Would it make more sense to take a train from York to Edinburgh and then day trip to Hadrian's Wall? Using a bus then? Or another train?

I like the idea of visiting Pitlochry from Edinburgh, but I'm not sure we'll have the time to go so far out. Any suggestions for closer day trips?

We were thinking a car would make sense as we'd like to use it to see
the sights around Bath (Stonehenge and Avebury, as well as a drive out
to Cheddar Gorge), and then drive through the Cotswolds (staying a
night or two to explore the area - Chipping Campden/Stow-on-the-wold),
up to Derbyshire (want to visit Chatsworth Estate), a night over in
York (a business meeting there), and then thought that it would be
easiest to drive from York to Edinburgh so as to be able to visit
Hadrian's Wall. Would it make more sense to take a train from York to
Edinburgh and then day trip to Hadrian's Wall?

That actually sounds pretty good to me. For a journey such as that it seems to me that a car fits fairly well. It wouldn't be a good use of money to have a hire car and do train trips at the same time.

You might consider going home from Edinburgh instead of having to go all the way back to London unless you need those days at the end for discovery of London.

It is not clear to me which country is your home country, therefore I am unable to suggest if you will need an IDP International Drivers Permit along with your home driving license. For certain countries, such as India, it is a mandatory requirement.

The idea of the Caledonian Sleeper to return to London is a decent one, or there are very fast daytime trains on the Virgin East Coast line into Kings Cross.

Just make sure you rent a car that is big enough for not only all the passengers, but for all their luggage to fit in the trunk. This often means renting a larger car than you initially thought - at a higher price. But it's worth it, so you can hide all your luggage out of sight when you stop (and so you can fit it in the car period).

Alright, roughed out itinerary…

Fly into London, go directly to Bath
2 nights in Bath
2 nights in the Cotswolds area (too much time here?)
1 night in York
2 nights in Edinburgh
2 nights in London

Does that seem like a good amount of time in each of these places? Or would you divide up your time differently? We don't want to spend more than 2 nights in London for sure, we are more interested in the other areas. We enjoy history, nature, old cities/buildings, food...

Yes East Coast of course - I blame the disorientation of having spent four hours on Cross Country Trains when I wrote that.......

You have a lot of traveling proposed in a very short timescale. For instance, your 2 nights in Bath means one day there before you move on. York to Edinburgh will take 3 or 4 hours depending on whether you take the train or drive, so that again will reduce time there.

Check that your car hire price includes your one way drop off fee, as it doesn't sound as though it does. I have been charged £60 for dropping a car in Glasgow airport 10 miles from where I rented it in the city centre. The hire price sounds very cheap. Does it include insurance?

Getting the sleeper train will save time, but it may mean you arrive having had no sleep if you are a light sleeper.

If I were you I would be sure and get full insurance coverage with no deductible. I have rented several times over there and always do that. Up in the lake country one time I ruined a wheel and tire on a Mercedes and it would have been close to 2k if I hadn't of had full coverage. They just replaced the car - no charge. If you don't have that they will put a hold on your credit card for whatever they feel it would cost. I didn't ask for the Mercedes, but they offered me a free upgrade because they were out of smaller cars. You need as small car. I would also recommend a gps. I use a Garmin with the proper maps installed. I have always used a standard transmission, but if you are not used to that, forget it, that is not the place to learn. The full insurance may cost the same as your rental.
Good luck - Bill

Fly into London, go directly to Bath,2 nights in Bath
2 nights in the Cotswolds area (too much time here?)
1 night in York
2 nights in Edinburgh
2 nights in London

I would drop York and Edinburgh and concentrarte on the area around Bath such as a trip to Tintern Abbey in south Wales or a trip to the coast such as Lyme Regis just to name a few places close by. If you are based in Bath you can do these and other destinations as a day trip. I would pick a location in Bath or the Cotswolds instead of 2 days in each. Save York and Edinburgh for your NEXT trip.