What is the comparison to a bird from Egypt?
Radak: Those in Egypt will move to return to their land like a bird moves to return to its nest. Just like man's wandering was compared to a bird's - "k'Tzipor Nodedes Min Kinah Ken Ish Noded mi'Mekomo" (Mishlei 27:8), so his return is compared to a bird.
Why does it add "and like a dove from Eretz Ashur"?
Radak: Those in Eretz Ashur will move to leave it to return to their land, like a dove moves to return to its dovecote. So it says about returning from Galus - "vecha'Yonim El Aruboseihem" (Yeshayah 60:8). The verse mentions Egypt and Ashur; the same applies to other places. It mentions the places from which it thought to receive help, and stumbled in them and were exiled to there.
Malbim: Some doves recognize their place from a great distance. "Ha'Ovedim b'Eretz Ashur" (Yeshayah 27:13) - they are called Ovedim (lost) because they were distanced greatly. Also they will rush to return to their nest.