Hi there Ashley!
Thanks for popping by the Disney Parks Moms Panel!
You can indeed bring your child's stroller on board on Disney Transportation Buses. You'll be required to have the stroller folded up prior to boarding the bus. On certain other modes of transportation such as the monorail and the larger boats, you'll be able to have your child remain in the stroller and wheel it right on board!
Getting to
Cape May Café for their fabulous dinner buffet will require transportation to Disney's Beach Club Resort. If you'll be in the parks prior to dinner, it's as simple as boarding a bus headed to that resort location! If you'll be back at your own resort prior to dinner, you'll need to take 2 modes of transportation to get there. You can take a bus from your resort to the theme park (or Downtown Disney) that is closest to you. Upon arrival, simply transfer to a bus headed to Disney's Beach Club Resort.
Alternatively, take a bus to Disney's Hollywood Studios. Upon arrival there, head straight on down to the boat launch which will take you to Disney's Beach Club Resort. Be sure to allow yourself a full hour of transportation time to reach your dinner reservation.
As one final option, if you happen to find yourselves in Epcot on the day of your dinner reservation at Cape May Café, you'll enjoy a short walk from the International Gateway straight down the walkway to the Beach Club. The walk will take about 10-15 minutes at a leisurely pace.
If you have more questions about your upcoming visit, be sure to stop by the Moms Panel again any time you wish! We love to hear from you!
Wishing you a simply Magical time at Walt Disney World!
Kirsten