Daenerys would have kept going once she realized that no one she knew was in this cart, but she hesitates. This is the first person to call her 'my lady' and treat her with some kind of respect, instead of yelling at her, after she barged in.

"You startle me? I am the one who barged in on your," she hesitates, what is this even called, "odd carriage. Please explain to me what this is and where we are headed," she speaks mostly with authority, her voice only shaking a bit at the prospect of being killed.