Here's something interesting. It's from LISTSERV 14.4
Originally Posted by jctgf
A 75-year-old Englishman in one of my classes corrected me vehemently when I pronounced the sentence "Mother bathed the baby" as if they verb were 'bathe' rather than 'bath'. He insisted that you 'bathe' in the sea, but you 'bath' in a tub, and he made out to be telling me (the American) how to pronounce the language 'correctly'. He turned to his 21-year-old classmates for support, and most looked at him like he was crazy--they say
A few months later, my 70-something aunt (originally from western NY, but a 50-year resident of Indiana) was over for a visit, and she told a story in which my grandmother 'bathed the baby'--pronounced like 'bath'.
So, this suggested to me that the difference might be not so much regional/dialectal as it generational.
However, dictionaries do treat this as a dialectal US/UK difference. AHD4 has no verb entry for 'bath'. MW9 treats it as "British". NODE (UK) gives have-a-bath senses (note: Brits have a bath/shower/walk, rather than _taking_ one) of both 'bath' and 'bathe', and treats the 'bathe
in the sea' sense as 'chiefly British'.
Read responses here http://listserv.linguistlist.org/cgi