Most of the analysis of this section that I've read works from the assumption that the point of view of the first half is Gertie McDowell's, but I don't think so, for a couple of reasons. Instead, I think the POV is Leopold Bloom's, as he imagines what Gertie might be thinking. There are a couple of giveaways, I think.
First, Gertie gives us a couple of times reasons why she won't run down the strand with the others. It's only when she stands up that we realize the real reason is because she's lame. We come to this realization at the same time as Bloom does, because he's watching her. Second, she reflects that Bloom looks a bit like a movie star. Since nobody else in the book seems to find him particularly movie-star-like, I submit that he's projecting that thought onto her; he doesn't just want her to think that he's Jewish-looking, rather, he's dark, handsome, and mysterious.
This is important because Bloom makes Gertie complicit in his own "release," and many commentators talk about the way Joyce combines opposites, with the connection of Gertie to Mary, and at the same time her connection to Bloom's issues. But I think that the opposition is inside Bloom -- we see how conflicted Bloom is in the "Circe" chapter, after all.