I think that the man would pay for the first date if he asked me out first. I would pay if I asked him out.
After that, we can alternate. But hey, if a man is offering to pay the bill ALL the time because he is old-fashioned that way, then I won't hold him back. It just means that I have to get him gifts or prepare some home-cooked meals to show that I appreciate that gesture. I feel really uncomfortable if a man pays for me all the time.