45 minutes to the parks? My oh my... Rest assured... it's nothing like that.
The All-Star Resorts have very good transportation. Approx travel times are as follows:
MK: 14 mins
Epcot: 10 mins
Studios: 9 mins
DAK: 8 mins
DTD: 17 mins
Of course, travel times may vary according to traffic, and other concerns.
During the morning, we do operate Magic On Demand out of the All-Stars... busses get dispatched on a demand basis... often times, the bus will only pick up at one resort, and then head straight to the theme park.
After 10:45am, busses convert to Flex Dispatch... The MK will always have seperate busses. Epcot combines the All-Stars until park closing, then splits them. Studios, DAK, and DTD always combine them. Depending on how the bus was dispatched, it could very well go Sports -> Music -> Movies.... or it could go Movies -> Music -> Sports.
One thing I will tell you... during peak times of the day, do expect crowds. The All-Stars have almost 6,000 rooms... so that is a lot of people. If you wish to avoid the crowds, try to avoid hot times to leave the park. For example, when the park closes, and they have fireworks... hang back for a half hour... then come on out... lines will be a LOT shorter.
Another suggestion... The infant may remain in the car-seat, however, the stroller part will have to be folded prior to boarding the bus. My advice is that while waiting in line for the bus, get everything all set, and ready to board. That way, you won't be scrambling at the last minute, dropping things, and whatnot.