Don’t worry if your bus is not as punctual as you might wish, the bus will show up! But if you plan to go a little further than only around the city, please check at the bus station in the port of Chios City if there is actually a bus coming at the day you want (especially in winter the weekend is sadly not that well connected but during the working days you should not have a problem!).
If you are not convinced to personally go to the bus station, here is why: the buses that drive further than just around Chios city and Vrontados are from a different bus line and therefore run a little different than the in-city-buses. So just take a bit time and check before your trip to make sure everything goes like you want it to.
Speaking of the bus station: right across the street is also the tourist office so you can kill the waiting time with going through all kinds of cultural and educational announcements and take some informative maps of the Island with you, when you are already at it.