The speaker is observing a moment in nature; she watches, undetected, as a bird happens upon a worm, which he bites in half and eats. The bird then drinks the dew from "a convenient grass," meaning that just like happening across the worm, the bird happens across a well-placed stalk of grass that offers moisture for him to consume. Though the events seem random, to the speaker, it seems to suggest an object lesson about how Nature has its own order. Animals live their lives opportunistically and manage to thrive without planning each move the way a human being might.
The word "convenient" is a value placed on the stalk of grass by the speaker; this is not necessarily how the bird would think of it.