My family of four will be in Edinburgh next spring to visit family and friends. We have seen quite a bit of Scotland and London, so, now are contemplating other areas of the U.K. to visit. I would like to see Bath and would be interested in recommendations for the best way to get to Bath from Edinburgh. Cost is not a big issue. Convenience is. I still need to keep an eye on my youngest, who is 11, all while hauling luggage around. Do we need to go through London?