So by clicking multiple check-boxes on a dating web site, you're implicitly reserving the right to decide on-the-fly whether these initial encounters are just "friendships" where everybody goes Dutch or "possible hook-ups" where you're okay dropping a little more cash? Would that mean that your date is also afforded the same luxury? What if her reticence to offer to pay was motivated by a decision to consider you "just a friend" and not worthy of dropping more cash on? Perhaps she was simply exercising the rights you reserved to yourself.
There's a real simple solution to this conundrum. The person who extends the invitation to hang out, no matter how casually it's made, is on the hook to pay for the group's expenditures. This holds true regardless of race, gender, religion or sexual orientation. If someone else steps up freely to help with the bills, that should be a pleasant surprise and not an expectation. This has the benefit of making sure that you only extend invitations to spend time together to people who are really worth it, and removing any awkward moments related to who pays the check. If you want to hang out but can't afford to extend an invitation, don't then accept one as a form of charity; make sure you spend at least as much time filling your own wallet as you do emptying someone else's.