Hi Stephanie! Sounds like you have some great dinner plans!
To reach Boma from Disney's Hollywood Studios, you would take an Animal Kingdom Lodge resort bus from the park. The bus ride takes about 20 minutes, and you may have to wait up to 10 minutes for the bus to arrive, so I would plan to be at the bus stop no later than 4:15 p.m..
Getting to Planet Hollywood from the Animal Kingdom is a little trickier since there are not buses running to Downtown Disney from the parks. You'll need to catch a bus to one of the resort hotels, and then transfer to a Downtown Disney bus. The quickest route would probably be taking a bus to the Saratoga Springs Resort and then taking the Downtown Disney bus. Because you'll have to change buses, I'd allot at least an hour for this trip, so plan to leave Animal Kingdom by 4:30 at the latest.
If you're driving or taking a taxi, both of these trips would take approximately 20 minutes, so you could stay in the parks a little longer.
Hope this helps! Enjoy your dinners!