It was a dedicated "right to the BB" turbolift, so I don't see why it wouldn't be pretty fast.I like to think that Apollo’s species resolved their interpersonal conflicts with giant-green-hand boxing matches.
EDIT: Regarding saucer separation, I thought it was very strange that the officers transferring to the Battle Bridge wouldn’t immediately site-to-site transport there, instead of wasting precious seconds or minutes going there by turbolift.