1

If there is a local public transport to Udine you can catch the eurolines.com coach to Vienna.

2

Local bus to Bolzano, train to Vienna either via Innsbruck or Salzburg. From Salzburg I think you can go direct to Bratislava

3

In the case you should not be interested in the huge detours mentioned above, take just a bus to Toblach and go on from there by train (change at Innichen, Lienz and/or Villach).
For example:
Cortina d'Ampezzo dp 08.05 - Toblach 08.45/09.06 - Vienna ar 17.28
Cortina d'Ampezzo dp 13.05 - Toblach 13.45/14.06 - Vienna ar 23.28

If you prefer to travel during the night, there are 3 possibilities (other timetables on Sundays and holidays):
Cortina d'Ampezzo dp by bus at 17.05 - Calalzo ar 18.03, dp by train 18.53 - Ponte nelle Alpi 19.03/19.51 - Conegliano 20.33/22.05 - Vienna ar 8.22
or
Cortina d'Ampezzo dp by bus at 19.20 - Calalzo ar 20.18, dp by train 20.36 - Venezia Mestre 22.53/1.13 - Vienna ar 8.34.
or
Cortina d'Ampezzo dp by bus at 19.05 - Toblach ar 19.45, dp by train 19.55 - Innsbruck 23.54/1.14 - Vienna ar 7.14

Edited by: neckervd

4

Thanks all, esp neckervd for the detailed reply.