When you only just start a new game, go to Riverwood and pickpocket Delphine (usually at the inn). You'd best save the game beforehand since the odds of a succesful pickpocket are low. She often carries an Orcish or (very rarely) an Ebony bow.


Not sure if this was already common knowledge, but i thought i'd mention it anyway.

I wouldn't recommend using the reload button if you fail when you do something and you don't need an orcish bow right at the beginning of the game, any bow will do.