Consider this, if you do get in a relationship with a girl that is as quiet and as timid as you seem to want her, how well will the communication between the two of you be? The relationship is doomed to fail unless you both change yourself for the relationship, and in that case you're moving beyond what your current fantasy seems to be.

So... just letting you know that your current fantasy is probably a pipe dream. The most you could get out of it is some sex, nothing lasting. But even sex would be a long shot since, if she's that shy and timid, she won't be that easy either.