Indeed, this usage of ござる is very stereotypical of period dramas, but I would caution against reading too much into its historical accuracy, even ignoring any dialectal considerations.
As far as I know, polite speech dates back to Heian times, at least, with stuff like はべり, and the modern-style ます was already in use in late Edo (in fact, even in early Edo). Anecdotally, this seems to match the observed development of contractions such as ござんす from ござります, which we have discussed recently in another thread. Anyway, I would expect actual people from the era to use polite speech whenever appropriate, with ます.