Fast travel to the Isengard map stone as any hobbit to begin with. Once you're here, change your character and fast travel to Isengard again (no need to travel anywhere else and back).
The list of Hobbits required are Bilbo, Frodo, Merry, Pippin, Rosie, and Sam. Rosie can be found at Hobbiton, Bilbo can be found at Rivendell and Hobbiton (old). These need to be purchased, whereas the main 4 are available from the beginning.