The only way to transport between Ireland and England in 1800 was by boats and ships.

The Ulster Transport Authority was dissolved on October 1, 1966, when responsibility for public transport in Northern Ireland was transferred to the Northern Ireland Civil Service.

By Bus Ireland, you may mean Bus Éireann. They can transport you to many places in Ireland. They operate services between the towns and cities around Ireland, and some services in some of the cities. A company called Dublin Bus looks after the routes for Dublin and its suburbs. See the Bus Éireann website below.

Rent a car and drive, public transport in ireland can be expensive if the ticket is not booked quite some time in advance.

That will depend on where you are coming from, what route you are taking and what method of transport you are using.