To get from Port Orleans Riverside to the different parks, it takes approximately the following times:
Magic Kingdom 25-30 minutes
Epcot 20-30 minutes
Disney's Hollywood Studios 20-30 minutes
Disney's Animal Kingdom 20-30 minutes
However, these times are just bus transportation times.Waiting for the arrival of the bus will add additional time. When I was at WDW in June and spoke to a cast member from transportation, he shared with me that the most you should have to wait is 20 minutes for a bus. Since you will be visiting during a very busy time, I do want to caution you that you may have to wait longer for buses since you may not always be able to get onto the first available bus.
If you do want to expedite the time to get back to your hotel to freshen up before dinner, you can always opt for a taxi.
Have a wonderful trip; you will be visiting during one of the most magical times!