Thank you for the question! There are quite a lot of ways to get to Budapest from Vienna International Airport. I guess it is important to get to Budapest as soon as possible since you write fast. We will still write some different solutions and in the descriptions we will describe whether we believe it is a fast or a slow solution, and the pros and cons with the different options.
1) Bus with Orangeways
Orangeways have a great bus service and the prices are very good. Normally one person from Vienna International Airport to Budapest will cost about 3500 HUF, which is close to nothing for this distance. The pro is that the bus stops at the airport and will take you to Budapest in an easy and quick way without many stops before arriving to Budapest. The negative is the fact that the bus only departs 4-5 times a day, meaning that you might have to wait for a while before your bus actually leaves. More information at orangeways.com
2) Bus with Eurolines
Eurolines is another option if you want to travel directly with bus from Vienna Airport to Budapest. They are a bit more expensive, but their buses leave at different times than the Orangeways buses, so you could choose the company with the departure time best for you. More information at eurolines.com
3) Train to Vienna and from Vienna to Budapest
This is a slower version because you will first have to travel to the center of Vienna and then from there to Budapest. This is for sure also the most expensive version, but if you prefer train to bus, you could consider this. The City Airport Train costs 12 Euro (the same as the bus ticket with Orangeways to Budapest) and takes you to Vienna in about 15 minutes. There you will need to get to the right railway station (using for example public transportation) and travel from there to Budapest with train.
4) Private transfer
There are quite some companies arranging private transfers between Vienna Airport and Budapest. These cost more, but they are the most efficient way to arrange this transfer if you are willing to pay for it. If you want this you can contact us and we will send a driver for you. Parts of the payment needs to be done beforehand. The price for such a transfer for two persons is 70,000 HUF, for three persons 75,000 HUF and keeps increasing with amount of persons. If you want this, write us an email!
We hope these answers will help you and wish you a pleasant stay in Budapest! For more information about Vienna, why not visit the Vienna Guide?