Aaron I am not an expert but since I have similar experiences I would like to give you some hints.
I think calling is better than texting because it will be more difficult for her to reject you when she talks to you. Also you can create a good mood in her by being nice and by using humor so that when you ask her out she would be more likely to accept. Don't ask her out straight away, always talk to her a bit and then say "I am going to blah blah on this day and/or this day. I would like you to come along. which one suits you the best?... ah .. I need to mention that I want you to come alone". If you give her options she won't be able to reject you but if you give her the chance of saying NO she might say NO.
Many girls leech on guys and take advantage of them. When a girl finds a guy who happily spends time and money on her in order to impress her, she will try to take the most of it. That's why she is bringing her sister. The thing you can do to 1- save yourself and 2- test her, is to ask her to go to a park or to the beach with you. If she refuses a simple activity date such as walking in a park or visiting a local market etc then she wants to take advantage of you. If she really wants to get to know you she would not mind a low-cost activity date.
If you set your date for during the week, Friday evening, or Saturday evening you will end up spending so much time and money. So try to take her to a park, beach, local market, gallery etc either on Saturday morning or on Sunday. If she says no, put her in your "sh1t girls" bin and move on. I promise if you spend 10% of the energy that you use to get this girl on another girl you will get a better result.