Gentleman, you pick up the cheque when you’ve asked someone out for coffee, dessert, drinks or dinner. If you extend the invitation, it is your responsibility to pay.
If you’ve no money whatsoever, buy a bottle of wine, some cheese and a baguette and ask her to join you for a picnic.
On to the grey areas.
If it’s a guys’ night that you’ve instigated, tell everyone that you’ll pick up the first round. If it’s business, casual or not, and you’ve asked to meet at a restaurant instead of at the office… in my book, you/your company buys.
If she asks you out, be charming, witty, attentive and please offer to pay as you’ve enjoyed her company so much. If she insists, accept graciously. Send a thank you. If you’d like to see her again, insist that you be allowed to take her out next time. It should go without saying that it isn’t done by texting.