Its officially for ALL regular public transport (only base fare, as said the usual supplements for fast trains/buses and seat reservations must be paid) and ONLY for EU-citizens.
I've already heard about busdrivers refusing the english as''you are out of EU''. And of course you cannot expect all 1000s of local busdrivers to grasp all the fine details of brexit etc. The English of course also stand out as you do not have the usual ID-cards that about anyone uses. As a general rule, poor old Ukraynian babushki's are also admitted for free though.
MAV-staff is nicknamed MAVia due to people erroneously trying to use this facilty for part-cover of international journeys. There are heavy fines for that. The simple answer is breaking up en-route. OR-to nearly all neighbouring larger towns (in RS, RO, SK) there are so many cheaper local fares, that it simply hardly makes any sense at all.
Bp-Bratislava (assuming you also have the free ZSR card) can be done for free by using local trains and walking Komarno-Komarom (about 3 kms), or for 1,80eur by going before Bp-Szob, buy the cross border (its a return in fact) to Sturovo and the either wait for the local train (long time) or use the EC you sit in and have to pay 1 eur extra to use that. You can do a more touristy trip via Esztergom (railway now electric), use local bus to Sturovo (DK if thats included, its a 2-hourly Hungarian Volan, but mo-fr only) that connects into 2 hourly EC-trains onward.
Bp-Wien is cheapest, not fastest, by going via Sopron (buy local VOR ticket onward from machine on Austrian platform there, includes also bus/tram in Vienna).
