Throughout our Croatian journey, we used the bus to get around, and the journey from Zadar to Split was no exception. You do not really have a choice to take a flight because there isn't one, however, the journey takes only 2 hours or so & there's wi-fi onboard (YAY!). We booked our ticket from the Bus Croatia website well in advance. I do think its possible to book it on the spot as well.
The main attractions in Split were within walking distance from our apartment ... so you definitely don't need fa car to get around. There are not many things to see within Split itself, so we did a couple of day trips we well (will let you know more in a separate post).