Whoever invited should pay.
Or you go somewhere thats free.
If you both decide you want to do something then split. But one will end up driving and having to pay for gas. It would be weird to have someone ask me out and them. They say oh can you pay me for gas. That just silly. Dont ask if you cant afford to do something. Or find free things to do.
I had people invite me to their birthdays and then expect me to pay for meal. Um you hosting it, so you provide at least something for your guests. Thats just courteous. We will bring gifts or BYO if you say its so, but some people wont come to a potluck if they dont have food to bring or dont have time to prepare anything. Also if its too far away some people need transport. It doesnt depend on if someone is a man or woman.
Nobody likes a bludger, its but from a womans perspective its somehow worse if the man asks you for money. Um no. And yes had that from a few. Please dont. If you want to be good husband material, then you provide.