The trains are operated by different companies (most countries have a national company and maybe a few private sector ones). There are also plenty of cross border services. But the timetables are worked out jointly because you can't have more than one train on a piece of track at the same time - and people want reasonable connection times if they have to switch trains. Slovakia only has one railway company for passenger trains and you could try emailing them http://www.zsr.sk/anglicky/contact.html?page_id=282

Bus info you could maybe get from Lonely Planet, either their forums or a paper copy of the relevant guide.