(b) That's right. It is clear that B is not promising to give A either money or a thing. But she is undertaking to do something that is a burden to her (because she wasn't until now obliged to stay open on Sundays). Furthermore, since A asks B to stay open, it is presumably to A's benefit to have shops in the mall trading on Sundays.
Either giving a benefit, or undertaking something burdensome or detrimental, is well established as being sufficient consideration for the other party's promise.