Gobstones has never received the publicity Quidditch enjoys, but I was most upset to learn that our victory was not deemed worthy of a single line in your paper, while you devoted half a page to an article about Puddlemere United’s new flying team bus.
-- Grugwyn Rufford, letter to the Daily Prophet (DP1)
The flying bus is a unique wizarding re-purposing of a Muggle transportation method. The first wizarding bus was the Knight Bus, founded in 1865 as an alternative for those who cannot be accommodated with Thestrals or brooms (DL).
The Knight Bus picks up stranded witches and wizards and transports them where they need to go (PA3). While not specifically stated, the Bus’s ability to move from place to place across the map in an instant suggests that its motion is a combination of Apparition and flying.
While the date printed on DP1 is 31 July 1998, the timeframe for these events is 1992-1993.
From the Web
Writing by J K Rowling on WizardingWorld (Pottermore): The Knight Bus
Mugglenet: Knight Bus based in fact?
Harry Potter Wiki: Knight Bus
Wikipedia: Magical Objects in Harry Potter: Knight Bus
WizardingWorld (Pottermore) feature: