The attribution of the pool to Bath has caused endless debate. The is chiefly because manuscript L has attached a 13th C. table of contents (though the detail may be older) which includes in a summary of this Wonder the additional information "in quo balnea sunt Badonis" ("where the baths of Badon are") (confusingly, in the translation left by Morris after his death*, this is added to the body of the text, though explicitly denoted as being from the table of contents by being in italics). Unfortunately, "Badon" is the site of a major battle which Nennius ascribes to Arthur, and the equation "Badon = Bath" has geopolitical ramifications for those who want to claim Arthur was born and lived in their part of Britain. It's better to ignore this and look at where the most likely hot pools are when deciding this Wonder's location (which is the tack taken here), but if you want know more you can find online summaries of the various debates from various viewpoints by McDougall* and Reno***