You can get from parkway station (2.5 miles by road from the airport) direct to Swindon in 26 minutes.
http://www.nationalrail.co.uk/
Don't go via Temple Meads, it's at least double the distance away from the airport and the train will take more nearly twice the time to get to Swindon. Take a look on google maps to see what I mean!
Why does Swindon have this awful reputation!?
It's awful!! For the last four months I've had the misfortune of going to Swindon a few times a month. The architecture, the roads, the town centre, the locals etc etc. Compare Swindon to Bath and you'll get the idea.
locals not so nice lookin.