Whatever your preference, let the shadchen know so it can be relayed to the other person.
Some people prefer that the man ask directly about a next date.
Others prefer that the shadchen act as the go-between throughout the entire process.
Others may start off with the shadchen as the go-between, and eventually decide together that they can arrange future dates themselves.
All are valid.
(btw, if you do ‘let go’ of the shadchen, it is still worthwhile to keep her in the loop, just in case you may need her assistance later.)
If you do decide to ask directly, you might ask right then at the end of a date. “I had a wonderful time. It was fascinating to hear about your trips. I am hoping that we can meet again. What are your thoughts?”
If you do ask directly, there is always the small chance that you might be turned down. That is all part of shiduch dating; you must be vulnerable and take emotional risks.
Know that you definitely are not the first person to have been turned down, and all people move on from it.
Accept it graciously and move on. “OK then, it was wonderful to meet you. I hope you do find someone who matches what you are looking for.” Your tone and body language matter.
Although it is typically the man who asks for the next date, the woman can let him know if you would be interested in meeting again. You might say things that give some indication of where you are holding.
“I’d love to hear more about that someday.” “If you are interested, I can tell you all about it sometime.”
To the woman:
Do not feel pressured to go on a next date just because he asked you.
If you really feel that you would rather not meet again, say so. Nicely. “I enjoyed our conversations. I learned so much about traveling in South Asia. I feel that we want such different things out of life. I don’t think we should continue meeting. I do hope you find someone soon.”