In what sense did Vasudeva become Siddhartha's guru?
Before answering this question, it's important to consider the different definitions associated with the word guru.
Guru1. Hinduism: a preceptor giving personal religious instruction2. an intellectual or spiritual guide or leader3. any person who counsels or advises; mentor4. a leader in a particular field
Now let's look at the character of Vasudeva and compare it to those definitions. Vasudeva is a poor man (a very OLD poor man) who runs the ferry. All of his enlightenment and knowledge come from listening to the river over which he ferries others.
“You will learn it," said Vasudeva, "but not from me. The river has taught me to listen; you will learn from it too. The river knows everything; one can learn everything from it. You have already learned from the river that it is good to strive downwards, to sink, to seek the depths."
Being one of the first to meet Siddhartha after Siddhartha gives up all of his worldly possessions, the two become confidants. Vasudeva's age and wisdom are obvious to Siddhartha. Enotes reveals that "Vasudeva becomes Siddhartha's friend and adviser" (which already lends itself to the definitions of guru).
Unfortunately, Vasudeva is already a very old man, and it isn't long after meeting Siddhartha that Vasudeva becomes so frail that he can no longer be a proper ferryman. It is around this time (and specifically after Kamala dies) that Vasudeva gives Siddhartha some important advice: to let Siddhartha's son go in order for him to explore life on his own. Siddhartha holds on for a while, and it is only when Siddhartha finally takes Vasudeva's advice that this trusted friend and adviser reveals all of the river-wisdom that he has gained over the years. The entire message of the river, that Vasudeva until this point has kept to himself, is of great importance. It is only after sharing this advice that Vasudeva, as guru, is "allowed" to head into the woods for his own death.
Oh yes, Vasudeva was most certainly Siddhartha's guru at this time! My very favorite quotation in regard to this is as follows:
This thought matured in [Siddhartha] slowly, and it was reflected in Vasudeva's old childlike face: harmony, knowledge of the eternal perfection of the world, and unity.
Now, how does Vasudeva fit the definitions of guru that are explored above? Well, Vasudeva certainly fits the first definition as "a preceptor giving personal religious instruction," although one must believe that the wisdom from the river could be considered "religious" in order to confirm that first defintion. Vasudeva fits the second definition as well: "an intellectual or spiritual guide or leader." Vasudeva is wise, smart, and breathes guidance for Siddhartha which, of course, is all through the river. Still, if you look at the quotation above, you can see the wisdom with clarity. Vasudeva fits the third definition, too, as "any person who counsels or advises; mentor." Although Siddhartha has other mentors in the future, Vasudeva is the first after Siddhartha has given up his wealth. To further this definition, the advice of Vasudeva is important in that it is only after Siddhartha takes this advice (to let his son go) that Vasudeva finally admits that Siddhartha has passed the test and reveals the secrets of the river. And finally, Vasudeva fits the final definition of guru as well. Vasudeva is most certainly a "leader in a particular field." What field is Vasudeva a leader in? Five words: the wisdom of the river.