Lydia never uses her bow though... I wonder if your using the pro wood elf archer wild hunter(riverwood)... obviously he is using his bow
Mine does, guess it depends on what you give her. My guess is that if you give her a 2-hander she will play more agressively and might not use a bow that much, as I said my current Lydia is only equipped with a one-hander and a bow and she will be using the bow until the enemy comes right up in her face.
Except that some followers are terrible with a bow and it would make sense for them to charge the enemy.
Most followers have bow skills + block skills, no matter what archetype they are.