Getting from Dublin Airport to Dublin Ferryport by public transport?

Irish Ferries operates a bus from Bus Áras. It's very infrequent but apparently it's in accordance with the ferry timetable.

Edit: the bus takes 15 minutes between Bus Áras and the Ferryport.

The 747 stops at Talbot Street, Talbot Place about 150m from the bus station. According to timetable it takes 30 minutes. Obviously traffic can change this.

Terminal 1 (Irish Ferries & Isle of Man Steam Packet Company) is the furthest out. I’ve walked it from Dublin City Centre, and it is possible, but it’s not a pleasant walk, nor a short one. Confusingly, Terminal 1 is also called “Dublin Ferryport”. It appears under this name on the Dublin Bus timetable and in rail timetables which include ferry services. However, all the signage in the Port area simply calls it Terminal 1.

• Irish Ferries services are served by Dublin Bus route 53B. Route 53B does not behave like normal Dublin Bus routes. For a start, it’s hard to find the timetable on the Dublin Bus website: you’d be better off looking at the Irish Ferries website or contacting them directly. Secondly, unlike most Dublin Bus services, they do give change, rather than refund bus tickets. Route 53B runs from Heuston Station to Busáras to Dublin Ferryport. Dublin Ferryport is the last stop, and the only stop in the port area.
• Dublin Bus route 53 is a normal Dublin Bus service which also serves Terminal 1. This does not specifically match up with the ferry times. Dublin Ferryport is the last stop.

Terminal 2 (Stena Line) is slightly closer to the city centre than Terminal 1, but not by much. Confusingly, Terminal 2 is also called “Dublin Port — Stena”. As with Terminal 1, this name does not appear on any signage, but rail information websites which include ferries do use it.

• Stena Line services are served by a private bus company: Morton’s Coaches. (Morton’s Coaches accept payment in both euro and pounds sterling, or did the last time I asked.) Contact Stena Line to enquire about timetables and pickup locations. As I recall, they pick up from Heuston Station, Conolly Station, and Westmorland Street. Conolly Station would probably suit you best — it’s just across the road from Busáras.
• Terminal 2, like Terminal 1, is served by Dublin Bus route 53. It is the second last stop, under the name “Alexandra Road, Breakwater Rd South, Stop 2269”. (I’ve never actually taken this bus, but so far as I can judge from the map, this stop is adjacent to Terminal 2. It might be best to ask the driver where to disembark for Terminal 2; in a worst-case scenario, it’s not too far a walk from Terminal 1.)

Terminal 3 (P&O Irish Sea), however, is merely a short walk from The Point, the terminus of the Luas Red Line tram service. You could pick up a tram from Busáras and then walk.

If your departure time does not align with any of the above services, The Point is probably the closest you can get by public transport. From there, you can walk or take a taxi.

All ferry companies operating out of Dublin Port should be happy to answer enquries along these lines. If you cannot find a suitable bus to meet your ferry, contact the ferry company; they’ll have all the information you need.

Both are North city BUT there are not direct public transport links between them. Dub airport is ~12k North of city centre. Ferry terminal ~4k East of city centre. The ferry terminal is not very well served by public transport - there are buses going out there from city centre.

I'm local in Dublin and it looks like google maps has the right options:

• 25min by car/taxi
• 1hr+15min by bus (to city centre then bus to ferry port - comprehensive details on bus in answer by @chx)

Cars can take the Dublin port tunnel which goes from M1 travelling south to near the port. There is a premium toll on this for normal cars during day as the tunnel is mainly intended to take big trucks out of city traffic.