'being asked' as adverbial

[joham]

And, being asked how and in what way, she answered: “I was in my house, and at midday a familiar came to me and told me to go with a little water on to the field or plain of Kuppel (for so is it named). And when I asked what he wanted ...

How would native speakers feel about the use of 'being asked' in this sentence? Could we also use 'having been asked' or 'on being asked' or simply 'asked'?

Thank you in advance.

[BobSmith]

[not a teacher]

Because it is out of context, it can be slightly jarring to jump right into "asked", so, to my ear, these are ordered from most natural to least:

having been asked
on being asked
when asked
being asked
asked

[TheParser]

***** NOT A TEACHER *****


(1) I think (think) that some books would suggest that "having been asked" would

only be appropriate if there was a significant time difference between the asking and

the answering.

(a) Maybe something like:

Having been asked the question last week, she finally answered today that ....

(2) If the answering immediately follows the asking, maybe "having been asked"

would not be a particularly felicitous choice.