In Bicentennial Man, Andrew (Robot) frequently address himself as "one" so many times?
I mean he uses this "one" word so many times in the movie?
Here is an example:
Andrew: Shall one get it, sir?
What is the significance of it?
It's a formal way of referring to oneself or rather it means "I" (or "you" depending on context).
In this case, it's effectively saying
Andrew: Shall I get it, sir?
One is a pronoun in the English language. It is a gender-neutral, indefinite pronoun, meaning roughly "a person".
For purposes of verb agreement it is a third-person singular pronoun, although it is sometimes used with first- or second-person reference. It is sometimes called an impersonal pronoun. It is more or less equivalent to the Scots 'a body', the French pronoun on, the German/Scandinavian man, and the Spanish uno. It has the possessive form one's and the reflexive form oneself.
He refers to himself as "one", not me. It was never addressed in the movie, it is a form of Illeism:
the act of referring to oneself in the third person instead of first person.
A common device in science fiction is for robots, computers, and other artificial life to refer to themselves in the third person, e.g. "This unit is malfunctioning" or "Number Five is alive" (famously said by Johnny Five in Short Circuit), to suggest that these creatures are not truly self-aware, or else that they separate their consciousness from their physical form.
Andrew starts his life as a "Household appliance" that is not supposed to be self-aware.