While flying from Budapest to Zagreb and then Pula (instead of directly to Pula) does seem a bit odd you should not rush with time estimate for a road trip as it will depend on great many things. Even without your transport being held up at a border crossing the roads towards the coast can be extremely busy in peak summer season (July and August). Especially on weekends and even more on the last weekend of July and the first of August as that's when Italians traditionally start their vacations and the Istria peninsula (Pula is the capital of the region) is the closest destination for them. Also, with a car/bus there's a risk of breakdowns, you may need to rest along the way (actually, if you have someone else driving you that is sure to happen).
So, the actual driving time is very hard to predict and if problems do occur there's often no real way around them and you could lose a lot of time. Flying, on the other hand, while still prone to problems and delays is generally more... stable. Anyway, jsut saying it can still make sense. If the price is of no concern.