Take the bus to the magic kingdom, then take the monorail over to the contemporary resort or you can also take the bus, I would say the monorail would be easier and quicker.
Done this many times myself, POP. Is my favorite value
There is no bus from MK to CR....unless, of course, they stuck one in to cover for the monorail not running. But with the boat and the ability to walk, a bus makes little to no sense.
I always take the bus to the MK, then walk over to the CR. It is almost always faster than taking the monorail. So, when you get off the bus, at MK, follow the herd out of the bus area. The vast majority of people will head to the left at the end of the bus stop area, you want to go right! You will see a sidewalk, underneath the monorail track....follow this to the CR. MK will be on your left, the bus drop off area on your right. Come to a street, push the pedestrian button, cross, and you're at the CR. Takes less than 10 mins.
If you were to take the monorail, you would follow the herd, they will turn off to the right to go to bag check at MK, you would continue walking straight, toward the monorail platform. Wait for the car to come, board and then hop off at the CR. It takes a few minutes to walk there, then a possible wait of 10-15 mins for the next monorail to come, 5 mins sitting there, then 5 mins to the CR.
Your choice.