The public transit intercity situation in Ontario is very unlike Europe. Depending on whether you want to travel directly from the airport, or from downtown, you will have different options and I predict you will not like any of them.
There are many different providers: Go train to Kitchener, VIA train to Kitchener, Go bus (horrible slow tortuous route), Greyhound, even a Federation of Students bus at certain times of the day. Some leave from downtown, so if you're arriving by plane you'll need to take the UP express first to get to Union. Others leave from the airport, or from assorted suburban locations, some of which are served by the subway in Toronto. The University of Waterloo has a travel page with various links you may find useful. Since you mention 25, I guess you are considering the GO bus 25 and have looked into how to get to it from wherever you are arriving or where you will be when your business in Toronto is finished.
Go does offer discounts to post-secondary students (on Canadian public transit, the undecorated word "student" means primary and secondary school, ie before university) but only if they are attending Canadian institutions. Your Hungarian ID will not get you a discount.