I often hear stories of people who go out again and end up getting engaged the second time around. My advice is to approach the shadchan and ask if he/she could contact the girl and see if she would agree to go out again. I don’t think there is a certain amount of time you need to wait, just have the shadchan feel it out rather than you calling her directly yourself. It is better that way because if the girl is busy or really would not consider it again, it is less awkward.
Hope that helps and hatzlochoh!