Different people act differently but if its me as a person A.. I would rather most welcome a person more to accompany my friend i.e person B, when I know I will be busy and would hardly be able to makeout some time for my friend.. it will be such a relief to me.
If I’m person B.. it depends what level of friendship I have with person A and will act accordingly. If he/she is a close friend..obviously I would tell her on the first place that I’ll bring a company along…if A is just an ok friend… I would excuse and won’t go!!