For reasons I won't attempt to explain, it has been taking passengers quite a while to clear immigration and customs at Heathrow and now other airports too.
Your travel options are:
1) Heathrow Express train to Paddington (London) from where you take a 90 minute train to Bath Spa train station
2) Railair coach link to Reading station from which you pick up the train from Paddington for a further hour.
3) National Express Coach service to Bath bus station
You can check train prices and the timetable at www.fgw.co.uk and the coach at www.nationalexpress.com.
Train prices are a complicated subject but, if you are able to restrict yourself to a particular train, an Advance single is usually a lot cheaper than if you turn up and pay on the day (though the super off peak tickets are also quite good value).
It is especially hard to predict how long it will take for you to clear customs, and advance tickets are not refundable (whereas offpeak and super offpeak and standard tickets are). In your situation I think I would either buy a flexible ticket in case of delays or travel via London with an advance ticket booked for much later in the day, take a shower, check my luggage into left luggage and spend a few hours sightseeing.
PS: At the risk of stating the obvious, there need to be 2 of you to take advantage of the "2 for 1 offers"