Most loot in Skyrim is level dependent to a degree - enemies/chests will not start carrying ebony gear until around lvl 36, for example.
Some of the sought after unique gear like Nightingale Bow will have different stats depending on when you obtain them. Enchantment aside, the base stats on the Nightingale Bow at minimum level are roughly equivalent to that of a Forsworn bow. And the forsworn are all around The Reach so you can probably grab one of their bows fairly easily.
Looking over The Elder Scrolls Wiki's entry on bows, there's a few areas where you might be able to grab an Elven Bow at low levels, and Glass Bows might have a low chance to spawn in boss chests even at level 6.
There is also supposed to be a guaranteed Ebony Bow in Lost Valkygg, but be warned that this can be exceptionally difficult for low-level players as there are enemies that do not normally spawn until much higher levels.
Alternatively; if your role-playing allows; if you get conjuration to 50, you can use a Bound Bow which temporarily gives you an ethereal Daedric Bow/Arrows.