conditionals - Is it correct to say: "I would do something, be it me"?

I mean that "I would do something, if it only were me. But it was not me, so I've done nothing".

Answer

No. It sounds old-fashioned, but searching through Google books for such phrases used in the 1800s, I did not find a single instance of anybody using "be it me" or "be it I" in this way. What you're looking for is "were it me" or "were it I"; this usage requires the past subjunctive and not the present subjunctive. Here are some examples:

Why, were it me, I'd take it just to spite him.

Were it me, I'd show him the difference.

Were it me, I do believe I'd be half inclined to stay, and be discovered.

"Were it I," said the second man, with a shrug of his shoulders, "I'd get it to the Admiral,"

I can make nothing of it, Roland, but were it I, I should ask my mother exactly what it means.

Were it I that sold that poor perished victim his drams, I should seem to hear his voice mingling its wailings with the storms of every bleak wintry night.

Some grammarian prescriptivists would say that it should be "were it I", but both forms seem to have been used. This is still an old-fashioned way of saying this, and I recommend saying "if it were I" or (maybe less grammatical, but more common) "if it was me" unless you want to sound like you're speaking archaic English.