Now I'm really confused. Wordref.com's dictionary includes use of Bonne continuation. Wordref was recommended by the native French speaker head of our teachers' association here in Victoria, Australia - so I'm guessing their info is pretty spot on. Tilt - whose 1st language is French - seems to find it OK. Montaigne finds it categorically OFF. Any other French speakers out there to jump on either end of this seesaw? And/or Montaigne, I'd be interested in your further elaboration as Jann requests.
Don't worry as opinions about Style and the like are different everywhere....it is not incorrect French at all and I don't think he meant to imply it was, it is just "formulaic" and "mechanincal" in that it is something to say to fill an awkward gap....native English speakers would just say "goodbye" or the equivalent....in some other cultures there are other ritual comments that you use after specific event like taking a bath...or before ...We brits would never wish anyone "bon bain" would we?
OK - many thanks - I can't get over how HELPFUL this forum is!! Even the negative info shifts my understanding (with the help of the clarifying comments added later : Thanks Tilt and Timboleicester and initially Jann too, for the perspectives you each offered) towards better understanding. In fact my adult community French class took me out to a French restaurant last night (I'm retiring). I made tiny cards to enclose in small cellophane bags with a few special chocs for each. Ended up wishing them 'une très bonne continuation dans vos études de la langue française'. I'm guessing that in this context - despite the fact I'm pretty fond of them all after a few shared years - that being a teacher-student context - the phrase may be appropriate for use. Huge thanks to all who've contributed here!