Every day is different, and times of day that you travel between destinations is different - but it's always a safe bet to allow at least a half an hour in each direction, if not 45 min. The buses "generally run about every 20 minutes, but you might arrive at pick-up with a LONG line and have to cycle through 2 or even 3 buses before you can get on. It's best to allow more time than you think you might need, especially if trying to make it for dining reservations. The actual travel time between destinations varies simply by nature of how far away the two points are from each other. AS resorts to AK will be shorter than to MK or DTD, for example.
For ADR's at character breakfasts before the parks open (i.e. Chef Mickey's at the Contemporary), check with the front desk when you check-in, but the buses will typically start running about an hour or an hour and a half prior to park opening. We had an 8 am at Ohana last trip, and got on the bus at 7:25 and made it with a few minutes to spare, after having to transfer to the monorail and then ride over to the Poly.