You can quite easily just travel about on your own to the places mentioned as they are all linked by rail with regular services. If you wish to visit Stonehenge, take a train to Salisbury - which has a wonderful medieval cathedral) - and then a shuttle bus to the stones north of the city.
Direct trains operate hourly between Cardiff > Bristol > Bath > Salisbury > Southampton & Portsmouth.
People on here have mentioned Mad Max tours from Bath to places such as The Cotswolds.
This is a re-seller for trains but the site works really well and charges a small commission:>https://www.thetrainline.com
This is the National Rail site which sends you through to the train companies to make bookings.https://www.nationalrail.co.uk
However, you can just rock up at a station and buy a ticket on the day although for longer journeys, this is likely to cost more. Play around with dates on the site above. Also consider getting a railcard.
Further advice on trains >https://www.seat61.com
This site is also good at telling you how to get about:>https://www.traveline.info/
Map of the rail network.