Would a girl try to talk to a guy she likes even if she is shy?

There is a girl that I always catch looking at me from a distance but every time she walks near me she avoids eye contact or quickly looks away. On the few occasions where our eyes happened to meet as we walked past each other she smiled at me and I smiled back. The fact that she avoids looking at me makes me not want to bother her but I'm not sure if she is just shy.

Would a girl try to talk to a guy she likes even if she is shy?
Post Opinion