The only Disney transportation offered at Pop Century is the Bus Service. To get from Pop Century to Boma, you have two choices. Drive, which would take 10 minutes; or take the bus to Animal Kingdom Park and transfer to a bus going to the Animal Kingdom Lodge which could take up to an hour.
You can get to both the Contemporary for Chef Mickey's and to the Polynesian for 'Ohana on the monorail. However, there is not a monorail connection at Pop Century. If you are going for lunch or dinner, try planning you day to be at Magic Kingdom or EPCOT, where you can take a quick monorail ride straight to the resorts. Otherwise, once again, you will have to take a bus from the Pop Century to either Magic Kingdom or EPCOT and transfer to the monorail; this will probably take 45 minutes-1hour. Best bet would be to drive if you are not at a park already, being about 10 minutes from both resorts.
Good luck, 'Ohana is really amazing and take some time to look around the Polynesian. Chef Mickey's is a classic (have eaten here 4 times I believe) and the kids will have a great time!
23rd visit March 20-25 @ Pop Century!
Have stayed at Polynesian, Beach Club, Grand Floridian, Animal Kingdom Lodge, Wilderness Lodge, PO Riverside, AS Sports, Music, Movies, and Pop Century.