an FTP connection to your server is required.
Connect to your server via FTP and stop it at the same time.
Now delete the new world in the "mincraftbukkit" folder. (Delete the folders world, world_nether and world_the_end")
Now move the "world" folder from the "minecraft" folder into the "minecraftbukkit" folder.
If you are using PaperMC now, the worlds are automatically separated into their respective folders.
Therefore I recommend to use PaperMC which you can activate under "Settings -> Change Version".