Bus service starts around 6:30am daily. This is to serve the guests going to the various early breakfasts throughout WDW.
I suggest you be at your resort bus stop no later than 7am. Earlier would probably be better as the buses don't run very often at that hour. If you just miss one you will have a long wait.
Your other option is to take a taxi from your resort. Taxis are normally waiting outside all WDW resorts. They are a fast and pretty economical way of getting around. If a taxi is not waiting at your resort the Cast Member working the outside podium will get one for you right away.