I used to live in Bath, if you're coming from the airport you'll probably want the Air Decker bus. The bus is pretty regular and the drivers are usually happy to let you off at any stop, it'll take you right into the centre of Bath and you can grab a taxi/train from the nearby station to Oldfield Park which has its own train station. I'd recommend buying your Air Decker tickets in advance if you do, it's cheaper and easier

The A4 bus goes from Bristol Airport to the bus station in Bath. It's a stopping service, and the stops on James West St are a bit closer to Oldfield Park than the end stop. It should be a short walk (10-15 mins) from one of the James West St stops to Oldfield Park by the looks of it on the map.

As others have mentioned, you can take A4 bus from the airport to get to Bath directly. If you want to explore Bristol first, you can take A1 to Bristol city centre and then take a bus or train to Bath from there.