Best ways of getting to Stonehenge from London that do not involve a tour

Salisbury is nearest station, and theres a Stonehenge bus every hour, the timetable is on the Stonehenge website.
You'd have to do Stonehenge first for your trip to work, and have an early start from London,its still an hour from Salisbury to Bath.

I know it would add to your day, but as long as you are going to Salisbury, you should definitely visit the Cathedral. It's not that far of a walk from the railway station; you can see the railway station and the cathedral (St. Mary's) on the second map here: http://www.salisburycityguides.co.uk/end.html

To do Bath & Stonehenge in a day is pushing it and not advised (virtually impossible). As already said, you would use the train from London (Waterloo) to Salisbury & then the shuttle bus (hourly) that run to Stonehenge. If you have just missed a bus, walk to Salisbury Cathedral - built in the 1200's & really impressive & take a later shuttle to Stonehenge. http://www.visitwiltshire.co.uk/explore/salisbury-and-surroundings

You probably would have saved money by staying in a hotel in Salisbury or Bath for 1 night rather than London.

www.visitbath.co.uk
Regular trains run between Salisbury & Bath. From Bath, you would go back to London (Paddington) though the occasional train* takes the longer route back via Salisbury. Fares are cheaper if you advance book, though the Salisbury to Bath leg would possibly stay the same - even pay on day.

Train schedules & fares here:- www.nationalrail.co.uk

www.firstgreatwestern.co.uk
* www.southwesttrains.co.uk

Thank you for the great advice! I will definitly look into Salisbury and the cathedral. Maybe we will do Stonehenge on a separate day. I really appreciate your feedback!

You've had lots of good advice. I would also say that Stonehenge looks exactly like the pictures, and you can't get close enough to touch. It's nice to have a full day for the sights of Bath itself.