He says he has important things he has to attend to, though we don't really know if it's true or not.
Gandalf noticed the ring turning Bilbo crazy so he forced him to give it up and leave it behind
The Necromancer of Mirkwood must be dealt with.
He made him leave the Shire with Frodo.
They notice that Gandalf has gone.
He 'left' them in Mordor. After leading them through the maze underground, they arrived in the final all. The Balrog arrived and Gandalf fell into the chasm blocking its path.
Lady Lorien saw the dwarfs and bilbo leaving, Gandalf knew that they thought he would slow them down so they left without him. Lady Lorien was referring to the fact that the dwarfs wanted to leave without gandalf.
He said “Don’t leave the path!”
Gandalf's presence with the group camped around the dwarven stronghold delighted Bilbo.gandalf
Gandalf was originally known as Gandalf the Grey. After his rebirth, he became Gandalf the White in replacement of Saruman. Gandalf the Grey and after his resurrection he became Gandalf the White.
I believe it was when Gandalf was leaving the group at the edge of Mirkwood.
Gandalf
Gandalf