Bristol Airport?

It depends where you're flying from. If you're coming transatlantic Heathrow and Gatwick are the nearest airports with those flights, meanwhile Bristol only has charter flights to Orlando. If you want to fly to Bristol, it would involve going with Aer Lingus or Air France/KLM and connecting, and those airlines may not be your best/cheapest option.

If you're flying from within Europe though then it's definitely a better idea than flying to the London airports if you can. Bristol has plenty of flights to continental Europe with budget airlines.

There is a direct bus from Bristol Airport to Bath. It is fairly slow but better than being tempted to go via Bristol.

You won't be able to fly direct to Bristol from California. You'd fly into Heathrow or Gatwick direct or connect elsewhere in Europe for the next leg to Bristol. I'd fly into London and make my way to Bath from there.

We flew AerLingus from Dublin To Bristol last June. Required to show US passport to board plane in Dublin. Only very small carry-on luggage permitted in the cabin. Normal carry-on checked at the gate. No immigration or customs in Bristol. Tiny airport. The car rental is a small building just out the front door. As luck would have it we arrived a few hours before the UEFA Cup Final in Cardiff. We got to wait in a long line with fans from Real Madrid and Juventus. The car trip to Bath is slower and more congested than I had expected.

Your idea is great but unfortunately no trans- Atlantic airlines fly into Bristol. Nearby Cardiff is trying to get trans-Atlantic flights and has a longer runway than Bristol so would be an ideal western gateway airport into Britain for those wishing to avoid the London area.

Anyway, it looks like you would have to land at Heathrow or Gatwick. From Gatwick, an hourly train service goes to Reading where you change trains for one going to Bath - usually every 30 minutes. If you land at Heathrow, you could take the shuttle bus to reading for the trains to Bath. Alternatively, use National Express coach service.

Trains > www.nationalrail.co.uk (Please note that it is cheaper to pre-book a specific train around 11 weeks ahead. If you find you can catch an earlier service - find guard at rear of train and ask if you can use the earlier train without penalty - they usually say it is OK).

PS. If you just put (From) Heathrow to BTH in the search box > it will show you how you can do it by train (click details).
If you put (From) Heathrow BUS to BTH > it will show you the bus link to Reading + train - all as one fare.

Don't dismiss the possibility of flying with Aer Lingus via Dublin to Bristol, if the price suits. Immigration formalities are effectively completed during your transfer and you arrive as an internal CTA passenger into Bristol.

Thank you for all of your comments. They are all very helpful.

Long ago, Continental flew direct to Bristol from Newark NJ. Although it was modern and convenient, it was a smaller airport, with relatively undeveloped local road access. It's not that hard to get to Bath from London, and there are so astronomically more flights to the three London airports.

The Aer Lingus service into Bristol is okay, often using prop-driven commuter aircraft (I did it from Cork). KLM is an alternative. It flies through Amsterdam to Bristol at a good price. I know Amsterdam seems out-of-the-way but what counts is the time it takes rather than the mileage. Either suggestion will surely be as fast or faster than getting a train at the vast Heathrow airport, and certainly less stressful. KLM is partnered with Air France and Delta from California. The KLM Cityhopper service from AMS also is on smaller airplanes. Bristol Airport is a busy secondary destination and the bus service to Bath should be easier than driving yourself.
Probably you want a multi-city itinerary returning from London or another gateway; easily calculated using a multi-destination search function.

SECOND THOUGHT: A subsidiary of Aer Lingus flies from Cork to Bristol. One non-stop daily, at a convenient departure time just before noon. Alternatives require a stop en route. Cork is an hospitable smaller city well worth a couple of days.

We have flown from Bristol to Dublin after a trip that ended in Bath.

One option is to start your trip in Dublin and continue on to Bristol the next day on Aer Lingus or Ryanair.

If you fly to Heathrow or Gatwick, you could consider a private car service to Bath. After your long flight from the west coast of the US, it might be nice not to have to deal with a train or bus trip from the airport to Bath.

Bristol is a smaller airport and not as many flight options. If I were doing the same trip, I'd probably fly into LHR and use a National Express coach direct to Bath. Depending on which coach you connect with, travel time will be about 2H:15M. You can use the time for a short nap to take the edge off jet lag.