home in?

[bartholomew]

Steve was quick to home in and was soon right over her.

[Quizmonster]

The phrase 'home in' is usually employed when speaking about a 'target' of some sort. In war, for example, a gun-crew would try to 'home in' on the enemy position by firing several trial shots, adjusting the position of their weapon after each to correct any mistakes. Once it is arranged...ie homed in...accurately, they can easily hit the target.

In your example, the 'target' is a woman and Steve is hoping to get close to her for one reason or another. So, just like the soldiers, he 'homes in' on her and manages to approach her very closely. 

[Clare A]

How very tactful, QM. I think our friend is reading a saucy novel!

[Quizmonster]

I did say, Clare, that Steve had approached the woman "for one reason or another". Perhaps, as you suggest, it was for "the other"!