You won't need a car in Bath, in fact it would be more of bind than anything (unless you were planning on exploring the countryside). The cheapest option is train - there is an hourly service, takes 2hrs 20 mins with one change (at Reading), with 'Advance' tickets costing £8.50pp each (£22.50 1st class). You need to order these tickets in advance and can purchase them 12 weeks before travel date. Book as soon as you can, as prices go up as tickets get sold. Allow plenty of time to get through immigration, etc
www.nationalrail.co.uk
The other option would be a private hire service - not too sure how much that would cost, but it would be a great deal more expensive than £34.