We have gone there with a friend of our's from Negril(he picked us up) who we met years ago when we took our kids with us and stayed at another resort. It is not a long ride(15 minutes maybe???) although an exact time is hard to pinpoint as we didn't go out until after 11 PM or maybe closer to midnight---no worries.
Can't really help you, because we never made it to The Jungle so far (we always get very lazy once we arrive at CSA, and besides that we'd rather not go if it's just the two of us). We heard CSA used to have a tour to The Jungle on thursday nights (ladies night), but they stopped doing that, because not many guests were interested.
My guess is that when you grab a cab, it's just a couple of minutes away from CSA.