Bus to Kinsale

None at all, this is effectively a City Bus Route. Even if you do buy in advance you do not have a reserved seat on the Bus Eireann route which is a turn up and go service.

There are 2 buses an hour on the route- the Bus Eireann #226 and the West Cork Connect #228

Be aware that the driver may only take cash (and maybe only exact change). If you don't carry cash, this can be a reason to buy ahead and have the ticket on your phone.

The buses also take credit and debit cards and the usual types of contactless payments.

Unlike many of the bus systems in America, which are buried far in the past, almost any bus in Ireland (or the UK) is firmly in the present.

Do any buses travel out to the Old Head? Missing that would be a shame.

No,

And you can't get out to the Old Head proper as it is now a private Golf Course, but this is what you can do- https://www.theirishroadtrip.com/old-head-of-kinsale-walk/#:~:text=One%20of%20the%20beauties

One can travel right up to the entrance to the golf course property, and the views from that extremely narrow strip of land are pretty incredible.

Not on the buses from Cork you can't- those end in Kinsale itself.

It is on a 3 times a day local service #253 from Kinsale to Clonakilty- https://locallinkcork.com/schedule/2-253-monday-to-sunday/