I think like five years.
Saul first appeared in Breaking Bad in I think the 8th episode of Season 2, but the first two seasons of BB only covered like two months in the storyline (and the show itself covered two years, even though it went from 2008-2013), so yeah, about five years. They can cover a shit ton of ground before getting to when Saul first met Walt and Jesse.
Personally, whenever Better Call Saul does end, I think it will cover his post-BB arc (which for non-BB viewers, you saw a glimpse of in the pilot's cold opening).