I just did this a couple of times this week (exit from plane to outside - did not go to Budapest).

Arrived on Austrian from IAD and accidentally left secure area after clearing Immigration, so went to see where Bratislava bus was, since I was thinking of going there during my 14 hour layover on the way back.

In the end decided to visit Vienna instead, so took the local (not the expensive 16 minute nonstop) and had more than enough time to walk around).

Both times it took no time to get outside.

Sounds like you will be OK as long as plane arrives on time.

Did see other buses as well, so I would think they are just outside of the terminal. At least the bus to Bratislava was a can't miss.