Is it normal to ignore a girl that likes me?

This girl at work likes me, as she always seems to want to talk and get to know me. Other employees confirmed that she likes me, as they said I should ask her out. They say that we would be a good match. But I always avoid her. If I do come in contact with her, I don't look at her and proceed to walk away from her. This has been going on for months now. I've done this my whole life when in school as well (I'm currently 20, soon to be 21). Multiple girls in high school tried to talk to me, but I always put my head down and tried to walk away when they looked at me. Some guys back in high school tried to get me to talk to girls, but I always went to the library or bathroom to avoid the situation. I also never had a girlfriend, never went on a date, and never had friends that were girls (as you can probably tell why). I also almost never leave the house (other than going to work or going somewhere to eat with family). I try to avoid social situations. I just do online college work and watch YouTube and listen to music just about every day. Anyway, I sometimes talk to other girl co-workers at my job, but never her. I think she gets upset and hurt when I do this to her. I also believe that she is waiting for me to talk to her, just like I do with other co-workers. BTW, I work at a restaurant. Is this normal?