Bus from Hvar to Stari Grad and Jelsa goes few times a day - during summer season more often... quite well connected to the ferry port of Stari Grad, and so it is to Jelsa, as the same bus goes till there. In Jelsa there is a ferry port as well, where the catamaran from Bol is landing on daily basis.
Reaching Jelsa it then becomes a round trip - a lovely 3 -towns-tour. If you get out in one of them, you can later on get the next bus to the rest of the tour
this 3 towns ( Stari Grad, Vrboska and Jelsa) apart from Hvar town, are -the- top destinations for day tour... a warning - the trip to the very end of the Island Hvar ( to Sučuraj) is not really recommended, as there are buses going only twice a week.
there are buses, but they drive not so often. For example I've been staying in Jelsa, we didn't have a car, so we had to take buses, but the evenings buses are driving not so late, the latest from hvar back to jelsa was e.g. at 6:30 pm the latest from stari grad to jelsa at about 10pm. So best thing is to go to hvar by car i think... then you can go where u want. because buses almost only drive from town to town, if u want to go to some beaches not near the towns, of which there are several very beautiful ones, u can't go. unless u rent scooters, bikes or a car.