Help them phase out.
Day 1: "Are you working on getting your driver's license?" Listen to her story.
Day 2: "It's actually not so anxiety-inducing to work on getting a license." Tell your story.
Day 3: "There might be some days I can't drive you. Do you have another way to get there on those days?"
Day 4: "I need to be there pretty early tomorrow...." Come up with a reason that is real to you, like art project set up, basketball, whatever. "I think you'll need to arrange another ride tomorrow." Most people won't object. If she does, smile and say, "Well, I will be around to pick you up at [early time]. I will wait three minutes, but then I have to go."
Day 5: "I promised to go in early and help [someone who you decided to help or got asked for help]. You may want to arrange another ride tomorrow." If she objects, tell her "I will be here at [early time]. But I can't wait longer than three minutes."
So on, so forth.
OR you could just say on Day 1: "I am not used to driving with other people. As a new driver, it kind of breaks my concentration and increases my chances of an auto accident. Also, sometimes I need to use this time to think about some things and make plans. I think it might work out better for us if you can find an alternate method of transportation for most of the time, and I just give you rides sometimes."