I agree with Emily. "This bus will lead her to the library" is correct but "This bus will take her to the library" is more natural sounding.

I would not say "The bus will lead her to the library", unless she were following along in a car behind the bus (which I'm assuming is not the idea you're trying to express). You could say "This bus will take her to the library" or "This bus route leads to the library".

"Lead" is used when the object is following the subject. "The bus will lead her to the library" and "If she takes the bus, she will get to the library" are correct, but "If she takes the bus, she will lead to the library" isn't as "she" is the subject of the sentence.