River isn't trying to be particularly stealthy when she approaches him though her steps are fairly quiet, finding curiosity in his interactions with the people around him. It's easy to notice how out of place he is -- out of time if you were specific, though whilst most people might not recognise it River has a special relationship with time. She's seen other people act similarly, not take being on another planet (or a different time zone) that well.

She blends in easily, browsing the market, making easy conversation as if she does this every day. It wouldn't be too far off the mark with how River spends her life. She doesn't quite know why she's following him, what specifically about him it is that causes her to quietly approach, leaning in with a hushed voice--

"I'd recommend this." She's holding up something innocuous, something entirely random that she'd just found on a nearby stall but it isn't the item that's important but a way in to a conversation -- a gauge of his reaction.