It's not clear if you booked a return or one-way. If you are traveling one-way there is no problem.
Should you have to gate check your bag it will be given back to you just outside the gate or plane in Vienna.
Normally all passengers are taken by bus into the terminal or deboarding is by jetbridge, everyone can either proceed to their connecting gate or the exit on their own. I'm not aware of passengers being shuttled directly to connecting flights, even so just inform the staff, Vienna Airport is an airport, not a prison, you are allowed to leave assuming there are no issues with immigration (since you're coming from with-in the Schengen Area). It would be polite to tell the staff on arrival that you won't be using your second leg so they don't end up waiting the aircraft for you to show up.
If you're worried about the possibility of using the return ticket there is more risk you'll be able to, last summer I was in the same situation with Austrian Airlines: I was on a non-refundable ticket ORD-VIE-BUD, BUD-VIE-ORD but plans changed and I needed to go to Vienna instead of Budapest. Upon arrival they were able to amend my ticket and cancel the connecting VIE-BUD and BUD-VIE portions so I ended up only flying ORD-VIE and returning VIE-ORD. The airline wasn't obligated to do this for me, so I consider myself very lucky that they were accommodating.
Alternatively, even with a discount fare, the taxes and fees (which likely were a significant chunk of what you paid) are refundable according to Austrian Airlines:
Similarly, any taxes, fees and carrier charges collected from you with the fare and shown on the ticket are refundable if the coupon is not used. This regulation also applies to non-refundable tickets.
It might be the most economical option to cancel the flight, refund the taxes and book a ticket on one of the shuttle bus companies or the RailJet train between Budapest and Vienna, tickets for these run €12-20, travel time is 3-4 hours, which isn't that long once you consider transit time to and from the airports on each end.