A is correct, at least it's what I would say!

Ela, better to say: I have to say goodbye now because the train is ready to leave in a minute.

Yes, in real life I used to listen people say "it's time to begin the first lesson". But, both ways are correct, aren't they?

A. is considered correct, and is not unusual in British English. Past subjuntive is used to speak about an unreal situation in the present, or immediate future (look up "second conditional"). In reality, it's very common to say C. at least here in America. I think this type of question is not really fair. Btw, in real life, you could avoid the subjunctive and say "It's time for us to say goodbye."