Rule of thumb: not just for dates but with friends, co-workers, etc.
Who invited whom? If you made the invite and have a job/steady income, it falls that you should pay. This is irrelevant of whether the person you invited is male or female. Some friends tend to split the bill in equal parts, but this is usually in a very close group, and not with co-workers etc. Others will insist on paying for their meals/drinks what have you. You should also take into consideration if the person you invited is employed and has disposable income.
Basically, if you asked that person out, falls on you to pay most of the time. If they insist in paying their share then readily decline, and instead plan for another outing where they 'can have' the check. IE: "I've got this one John/Jane, you can get the next one." This of course is not the right choice of words if you're on a date and it was pretty obvious that it did not go well. For a case such as that, pay the bill, and run as fast as you can.