I hope by now you have booked yourselves into the site recommended by others at
https://bathcaravanpark.com/ it is ideally placed to access the city and opposite the Newbridge Park & Ride. The return bus stop leaves from outside a small Tesco supermarket if needs be. I suggest you check it out on Google maps, walking into town along the river is a good option but may take up too much of your valuable time. You could consider walking into town via Royal Victoria Park (it has a botanic garden) which can start your sightseeing at The Royal Crescent, along Brick Street to The Circus and down Gay Street towards The Abbey, past The Jane Austen Centre and Queen Square, then The Theatre Royal and Kingsmead Square.
Having lived in Bath for 70 years I am more than happy to share any useful information with you but am struggling to know where to start. It looks as if you will only have a couple of nights so I am sure you will want to return another time. I do appreciate you are travelling from Northern Ireland. Bath has two Universities and a significant retired population as well as being one of the most popular places in the world for tourists. Hence you should find it vibrant and interesting. It looks gorgeous in the sunshine but if it rains just bring an umbrella you will still have a great time.
We have some fabulous parks, tennis courts & children's play areas within the city and plenty of excellent pubs, cafes and restaurants to choose from. 'The Architect' between The Abbey and Pulteney Bridge with a weir over the river Avon, next to our famous 'Rec' the home of Bath Rugby, is my recommendation for eating with plenty of seating options and good beers. Shopping is popular. Some great independent shops mostly at the north end of town and then past COS, Primark & Cotswold Outdoor down to the open air Southgate shopping centre with Apple, M&S, Zara to the south (public toilets). I recommend walking and stopping to admire the incredible architecture & buskers as you amble about.
We have a central booking office for events which take place every day so you might care to see if there is anything which takes your fancy either in advance or on the day if there are returned tickets.The Forum is an amazing venue, Van Morrison was there for 2 nights last week.
https://www.bathboxoffice.org.uk You will always find some live music somewhere, maybe Komedia in Westgate Street or The Bell in Walcot Street. We have great small cinemas - The Little Theatre & Everyman Tivoli.
Toppings next to The Abbey is a bookshop you could spend the whole day in, but worth a 5 minute look if that is all you have. They have visiting authors at multiple locations expanding according to the number of tickets sold.
Bath Fringe Festival runs from 22 May to 7 June.
https://bathfringe.co.uk/
The Holburne Museum in Sydney Gardens at the end of Pulteney Street has a lovely outside cafe for tea & cake etc and to rest your legs.
https://holburne.org/ Most tourists are looking for it because of Bridgerton on TV.
You can indeed try and book The Spa with a rooftop swimming pool. Again near the Abbey. Nowhere is far from anything.
https://www.thermaebathspa.com/
Enjoy your weekend and please do ask if you have any other questions. If you plan to visit The Roman Baths I would arrive early to avoid the queues.