Gatwick or London to Bath?
 

Which airport should I fly into if I am going directly to Bath? I believe it is about a 2 hour trip, is this correct?

If you are driving down to Bath, you would be better off flying into Heathrow than Gatwick. Heathrow to Bath would be less than 2 hours. Gatwick to Bath would take you around 2.5 hours. This is of course considering normal driving conditions with no serious traffic incidents on the motorway.

I will be taking public transportation - either train or bus?

I really can't comment about trains as I haven't tried getting to Bath from the airport, maybe someone who has done that can.....add in another 15 - 30 minutes to the above mentioned travel times for buses - this is of course true only if it is a direct bus, you may have to factor in additional 2 - 5 minutes per stop if there are stops in between.

There are direct coach services from LHR.

You can get a coach to Readin then take a train from there

You can get a train from Gatwick to Bath that avoids London where you change trains at Reading

The direct buses from Heathrow (www.nationalexpress.co.uk: every hour or two, taking on average 135 mins) are the easiest way to do this. Trains from Gatwick are hourly, but they're a bit grubby till you change at Reading, and they typically take a wee bit longer.

The bus from Heathrow to Reading station to catch a fast Bath train is usually fastest, but the transfer can be uncomfortable, and it works out a bit more costly than the alternatives.

I don't know if this is helpful, but the closest airport to Bath is Bristol. You could look for connecting flights.