Why not to give a girl a ride home from school

There’s this one girl I’ve had my eye on for the last few months. I see her probably at least every 3-4 days, cause I visit her roommates. I just haven’t really got around to asking her out. I know she dates a lot, but I’m not sure if that’s part of the problem. We’ve only really chatted a few times, but enough for her to know where I’m from etc… So, time for the funny story of the month. I see her walking towards where we live (we live in the same apt. complex) so I ask “you headed home? She replies “yes.” I ask “want a lift?” She replies “yes.” We start walking home. We chat about trivial things that would be of little interest to the average reader. We arrive. I park, and we both walk towards the middle of the complex. She asks “What was your name again?” I, not being too amused respond “Do you usually get in the cars of strangers?” and start walking in the opposite direction. She looks puzzled, and heads towards her apt.