A common misconception about Transportation is that the more you pay for the room, the better the transportation is. This is not true. You're paying a premium price for a premium hotel room. Nothing more. In reality, the All-Stars typically have the best bus service, followed closely by Port Orleans. On a side note, Port Orleans busses have a 97-98% on time rate, based on current statistics... this means that 970-980 busses out of a possible 1,000 busses have arrived on time. (Based on 8am-11am MOD dispatches, for a one week period)
As for the Contemporary...
The Contemporary is located right across the street from the Magic Kingdom, and is a 7-10 minute walk to the front gate. The Monorails depart from the Contemporary every 5-10 minutes, and travel to the TTC, Polynesian, Grand Floridian, and then finally the Magic Kingdom. Depending on who's driving the trains, it can be anywhere from 12-20 minutes to the MK.
To get to Epcot, you must switch trains at the TTC. Epcot trains run approx every 10 minutes, and it's a 10 min ride from the TTC to Epcot.
Busses run approx every 15 minutes to the Disney-MGM Studios, Disney's Animal Kingdom, and Downtown Disney. DTD routes always will be Co-Po-GF. AK Busses will only go Co-Po. Studio busses will do Co-Po until 11am, at which time GF is added as well.
From what I have observed in the past few months, busses typically have been running just fine from the Contemporary. During the mornings, and peak night time hours (ie: park closing) it is to be expected that both busses and the Monorail will be crowded. The Monorail also gets crowded during dinner exit times. At night time, the Downtown busses get crowded as people leave the MK, and head over to the Contemporary to catch the DTD bus. Extra busses are added to the routes to compensate during these times.