Travelling from Basel city centre to basal airport early morning 6am flight. Is there an airport bus that runs before 4am? Do we need to be at airport 2 hours before flight for international destination.?
There was a similar question a few months ago: https://community.ricksteves.com/travel-forum/switzerland/basel-getting-to-the-airport-early
The airport bus runs to/from the main train station, so depending on where you are staying, you'll have to get yourself there. The first bus is at 4:10am (you can check schedules on SBB website even though it's a bus). It's normally recommended to arrive 2 hours before your flight, and a few shops will open at 4am for morning coffee etc. It's not a big airport and at that time of day, you're probably ok taking the first airport bus, especially if you can check-in online. You'll be there by 4:30. If you're nervous about the time or not staying near the SBB station, you may want to just spring for a taxi. https://community.ricksteves.com/travel-forum/switzerland/taxi-service-in-basel
Do you mean an international destination, like Paris or Amsterdam, or a non-Schengen destination, like London or Dublin? I do not believe they have any intercontinental destinations, like New York or Toronto.