Hi Karen,
I love that you're looking to maximize the magic in your day! I will tell you that my family has been able to catch a bus after Rivers of Light at Disney's Animal Kingdom and make it to Magic Kingdom Park in time to watch Happily Ever After, but whether or not it will work for you will all depend on the actual show times for the day you'll be there.
Rivers of Light is a beautiful show full of gorgeous music, dramatic lights, and graceful water that lasts approximately 15 minutes. I'd factor in at least 15 minutes to safely exit the seating area and walk to the bus loading zone after the show is done. Then, a bus ride from Disney's Animal Kingdom to Magic Kingdom Park will take around 20 minutes in normal traffic conditions. Since you can count on buses coming every 20 minutes, as long as crowds are reasonable and you don't have to wait for more than one bus, it should take no more than 40 minutes total to travel from one park to the other. Be sure to allow a bit of time once you arrive at Magic Kingdom Park to go through security and ticketing. I'd say that if there's only one hour between the two nighttime shows' start times, it
could be possible for you to experience both of them, but you'd need a bit of pixie dust for a quick exit and a bus to practically be waiting for you. If there are two hours or more between the shows' start times, you should have no trouble seeing both of them. If you feel the schedule is too tight and you have to choose between the two, my personal choice would be to see
Happily Ever After as it's my very favorite nighttime experience at the Walt Disney World Resort.
Thanks so much for visiting us at the Disney Parks Moms Panel, Karen, and have a truly magical vacation!
Missy