Google Maps is giving me directions from East Dean to Bath via a train to London and then to Bath. My question is whether I have to take two different trains: one into Victoria station, then the Piccadilly, and a train from Paddington to Bath. Do I need to pay for the fare for all three means of transportation, or does one ticket include both stations and the Piccadilly?
You can buy a through ticket from any station to any station. When that involves a cross London transfer it automatically includes the cross London tube fare.
So, yes, this can be issued as one ticket. Just put Eastbourne to Bath into any train company app or website and it will bring up the fares.
To get from Victoria to Paddington you wouldn't take the Piccadilly line as that doesn't serve either station. You would use the Circle Line.
If you book a through Advance Fare (train specific) Eastbourne to Bath then if the train from Eastbourne to Victoria is late arriving at Victoria your ticket is automatically valid on the next train from Paddington if you miss your booked train.
Looking on 6 January (so not too far ahead) I can see through Advance Fares from £31.50 on the 0933 from Eastbourne, £37.50 on most others.
That is about as cheap as it gets, and is significantly cheaper than buying it as 3 tickets.
A railcard gives you 34% off those prices.
Thanks for the help!