On consoles like PS5 and PS4, you can thank the Battle Bus driver by pushing the down direction on the d-pad. If you're playing with a mouse and keyboard on a PC, then you'll need to press 'B'. It goes without saying that you'll need to ensure you're inside the Battle Bus in order to thank the driver, so remember to be courteous before leaping out onto Fortnite Island.
You can check you successfully thanked the Battle Bus driver by observing the social feed on the left of the screen. It'll display your username in a golden colour and say, "Username (level) has thanked the bus driver". Once you're happy you've thanked the driver, you're free to jump out whenever you're ready.