A question about transportation expenses.

Today, I went on my first dinner date and exchanged contact information with him, but I wasn’t given any transportation money when we parted. I had assumed that the man would hand it to me in something like a small gift envelope at the end of the date… I live in Setagaya, so transportation costs aren’t particularly high and it wasn’t a burden for me. But if someone lived in Boso, Chiba, or even somewhere like Takaido in Tokyo, I imagine the travel expenses could become a burden. I also wondered whether this might affect other female members, so I wanted to ask. A question for the male members: How do you usually give transportation money to the woman you’re meeting?