What does it mean when a girl takes a long time to respond after I asked her out?

[576]

I really like this girl. We have talked before but seldom meet in person so I asked her out in Facebook. Before that we were having a conversation on Facebook as well and she replied very quickly but when I asked her out, she took about 3 days and finally replied "sry for late reply! I can't cause I'm not allowed to go out alone with guys....sry! " I understand that I should have asked her out in person but given the circumstances, what could this mean? Was she unsure about me so she took so long to decide? Or could she have just been thinking of how to turn me down? Cause I read that if a girl doesn't like u, she would reply no very quickly.......( and I understand that she might really not be able to go out with guys but if tht was the case she would have replied pretty quickly rite?)

[June]

hey you never know maybe she was just about to reply then her internet connection broke down but anyways maybe you surprised her and she needed to think about it