Does "Sorry teacher, I have forgot my textbook" sound polite to native English speakers?
***** NOT A TEACHER
*****
1. In American secondary schools, some students would say "Sorry, sir / ma'am" or possibly "Sorry, Mr. / Miss / Mrs. Jones." In most cases, they would probably NOT use any title: "Sorry, I forgot my book."
2. If a student were to address a teacher as "Teacher" in an American classroom, the American students would immediately snicker (a disrespectful little laugh) and identify the student as a foreigner. (In ESL classes, almost all beginning students use the term "Teacher." By the time that they become intermediate students, they realize that such a term is not used in American classrooms. By that time, they have already become "Americanized" and are no longer so docile and respectful!)
3. If you do not wish to use "teacher" or "sir / ma'am" or the teacher's surname (last name), maybe one "solution" is to simply expand the sentence.
a. Instead of "Sorry, I have forgot(ten) my textbook," you could expand it to:
"I am very sorry, but I have forgot(ten) my textbook today." (Longer sentences usually (not always) sound more courteous and respectful than short sentences: No. / No, I won't. / No, I won't be able to attend your party on Saturday. / I am very sorry, but I won't be able to attend your party on Saturday.)
*****
In regard to that bus driver:
1. If he was answering a yes / no question, I cannot think of an alternative to "sir."
2. If he was asking a question or giving instructions, he could have used the term "young man":
a. "Excuse me, young man, would you mind helping that elderly gentleman get off the bus?"
James