Bus routes 8, 11, 26, 133, N8, N11, N26, N133 and N242 stop just a stones throw away from The Swan.
A short stroll away from Monument Tube Station, you can get off the train there and walk to The Swan Tavern in under five minutes. Bank Station is just as close by if you are getting the DLR.
Fenchurch Street Station is the closest National Rail station which is just a six minute walk to The Swan. You can also walk to and from the pub from Liverpool Street and Canon Street Stations too.