Yes and no. Bus service for character breakfasts begin thirty minutes before the earliest seating. The marquee on the bus will read "Character Breakfast." Guests should verify with the driver which park the bus is going to for the character breakfast because there are different ones for different parks.
Assuming you are staying at a WDW resort, the 'shuttles' you refer to are WDW buses....WDW Buses start running to the WDW theme parks from 1 hr before park opening to 2 hours past park closing. The exception is for Character Breakfasts - buses are from 0700 to 0800.
If you are staying off site, some hotels offer 'shuttles' to the Orlando area theme parks and the times and availability of those 'shuttles' vary depending on the hotel.
I've read several posts lately that the bus start time isn't always such a hard & fast rule. The recommendation was that if you are in any doubt, check in w/ the concierge & they will make sure the bus will be on its way to pick you up.
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