I think you had the idea of Aphrodite approaching Adley because there was something that caught her interest. At the moment, her cover is that she's a for-hire consultant/adviser and scholar... so writing things in a notebook isn't that unusual. She's also staying at a Harper-friendly inn (though no one knows that, obviously, lol) and simply waiting for some kind of missive or message to arrive, telling her what she needs to do next - which I'm assuming has to do with the mage somehow, gathering intel most likely.

Adley is a tad bit of a loner, but wouldn't turn someone away for simply sitting down and talking to her. ^.^