A Route of Evanescence (1)
The speaker is trying to document a brief, impermanent experience. The hummingbird flew into the speaker's sight, but doesn't seem to have left any evidence of this. Its path then, is one of disappearance. It's the strangeness of this experience (of something darting in and out of sight, in an instant) that inspires the rest of the poem.
A Rush of Cochineal (2)
This gets at how quickly the "event" went down. Dickinson could have described this scene in a million boring ways, but instead she tries to establish tension between the sense of being awestruck and the sense of time passing quickly. This happens in the poem as a whole but also in individual lines like this. "Rush" connotes speed and wind, in addition to being a short word that we can speed right past. But the word "Cochineal" stops us in our tracks and forces us to pull out the dictionary.
The mail from Tunis, probably, An easy Morning's Ride (7-8)
Here the speaker suggests that while a trip from Tunis to America might take a human being weeks (remember, we're in the nineteenth century here!), the hummingbird could knock that out quickly. Ho-hum. All in a morning's work.