One day she asked me if I wanted to go to the cinema and I accepted. I would say: one day she invited me to go out to a movie and I accepted. accepted is used in common usage just depends on what region you are in and who you are talking to I like accepted much better then Yes

You "accept" an offer and so this sentence is not bad. . It would be more natural to say "...I said "yes" ".

It is correct. You could also write "and I agreed" if it suits you.

It's kind of a good answer but you could also say "I said yes to her"