Hi there Joseph!
Welcome back to the Disney Parks Moms Panel!
Disney's Beach Club Resort is one of my favorite places to stay when visiting the Walt Disney World Resort. From your resort, the quickest way of traveling to
Disney's Spirit of Aloha Dinner Show at Disney's Polynesian Village Resort is by car. If you will have access to a car during your trip, I would recommend driving. If you will not have a car during your stay, you may want to consider taking a taxi if you don't mind paying cab fare. You can estimate your travel time to take approximately 10 - 15 minutes by car.
If you are hoping to utilize Disney's complimentary transportation, I suggest taking a bus bound for Magic Kingdom Park and then transfer to the water launch (water taxi) or Resort monorail bound for Disney's Polynesian Village Resort. I would allow at least 45 minutes for the travel time if utilizing Disney's complimentary transportation.
I hope this helps. Please don't hesitate to visit us again with any additional questions that you may have. Best wishes for a magical trip, Joseph!
Happy Travels,
Jodie