While the hunter represents human companionship, the white heron represents the companionship of the natural world. And to this end, the fluctuations we see in Sylvia's perspective on the heron represent shifts in her valuation of nature.
A nature-lover at heart, Sylvia loses track of her fondness for all things natural when the hunky hunter comes along, and decides to find the heron and lead him to it. It's a major change of heart, but what can we say? Love makes people do all kinds of stupid stuff. But anyway.
Like the lovely cow Mistress Moolly, the white heron becomes friends with Sylvia. So when she goes out on her own to find it for the hunter, though there are plenty of other animals around the oak tree, only the heron sits with Sylvia as they "watched the sea and morning together" (2.13). Although the two aren't able to communicate, their brief moment together has a big impact on Sylvia—afterward, she is unable to betray its location, and pulled right back to her connection with, and respect for, nature.
Maybe it's the fact that the white heron is rare and special, even to her. Maybe it's the passion stirred up by the mystical experience that she has atop the oak tree. Or maybe it's that Sylvia sees a little bit of herself in the white heron; passionately in communion with nature, despite the world of human affairs desperately trying to pull her back. No matter what exactly causes their bond, it's this bond that prevents her from telling "the heron's secret and [giving] its life away" (2.13). And when this happens, we know Sylvia's recommitted to her country ways.