Upvote:3
What I've found so far (most links are in Hungarian):
There's a map on the track's website that lists suggested directions. This is from 2016, but Volan's website (long-distance bus/coach company) approves this, these bus lines still exist.
So you can use Volan's 321 line from Újpest Városkapu (also, station on the "blue" metro line M3). This uses M3 motorway. If you're afraid of congestion, you can use H8 HEV line from Örs Vezér Tere to Mogyoród, and use one of the other options backwards (320, 321, 325, 326), or simply walk. Szilasliget (also a H8 HEV station) could also be an option. Örs Vezér Tere can be reached by the "red" metro line M2. (just to know: normal HEV tickets and seasonal tickets are only valid within the city, when you leave the city borders you need to pay some extra)
Taxis are regulated, there's a 300HUF/km fixed price, and a 700HUF base price no matter which taxi you use, and their cars look more or less identical (taxi companies fought united against Uber, that was the agreement in the end). You can even use price calculators beforehand to estimate what certain rides will cost. (e.g. Budapest Taxi has an Android/iOS app with in-built calculator)
You can rent or use your own car as well. In this case be sure to have a vignette for Pest county.
If you're really loaded, there's a helicopter service between Budapest and Hungaroring in that period. They take off from the river banks. (at least earlier years this was the case)
Are there dedicated buses running to the track? Does the regular city bus line run to the track much more frequently during "normal" daytime hours making it a much shorter trip?
I have no experience with F1 specifically, but other large events (kayaking, swimming, etc.), yes, this is the case.
Is there some sort of train/tram (that doesn't run this late in the evening)?
For me, Google Maps shows 1:02-1:28 long rides. You can set departure time, maybe that was your problem (Hungary uses CEST, so UTC+2 in August). In general, nighttime public transport is infrequent. There are night buses (the ones with 9xx numbers), and tram line 6. Night bus 992 goes there, but I don't suggest it.
Other suggestions:
If you arrive by plane, only exchange a small amount of money at the airport for your ride/ticket, even better, if you can get some at home. The money exchanger at the airport is a ripoff! Other changers tend to be all right.
It seems Hungaroring tickets are 15% off until the end of the year.
If you're from the EU, you can use your mobile internet here as well. That might come handy whichever travel option you choose. BKV/BKK has their own timetable app, but Budapesti Menetrend is also good for timetables. OTP's Simple app can be used to but vignette or pay for parking, and so on.
Oh, and of course in case of large events the timetables tend to change accordingly.
(I've never visited F1, but I live in Budapest.)