"Fyddi di gartre? Bydda."
Translation:Will you be at home? Yes.
Bydda means yes in this sentence yet in the previous sentence had a totally different meaning
This is one of the problems of translation. There is no specific word for 'Yes' or "No' in Welsh. The language uses various verb forms to show a positive or negative response to a question.
In this example a literal translation would be 'Will you be at home? (I) will.
So that is consistent with a sentence starting with "bydda'
eg 'Bydda i gartre' = I will be at home
The slight difference between 'bydda' in its own and 'bydda i' is that in the first the pronoun 'I' is implied whereas in the second the pronoun 'I' is obvious.