Hi, Miranda!
Great question!
We stay at Bay Lake Tower at
Disney's Contemporary Resort frequently, but love to visit
Disney's BoardWalk area, too. To get between the two, we'll typically head to Epcot in the morning, then walk over to the International Gateway (between the United Kingdom Pavilion and France Pavilion in World Showcase) for easy access to all things BoardWalk. To get to Epcot, take the monorail from the Contemporary to the Transportation & Ticketing Center; transfer to the Epcot line once there.
If that won't work for you, you could just walk or take the monorail to Magic Kingdom, which is right next door to your resort (good planning, Miranda!) then take a bus to one of the BoardWalk area resort hotels: Disney's Beach Club Resort, Disney's Yacht Club Resort, Disney's BoardWalk Inn. (A bus to Walt Disney World Swan and Walt Disney World Dolphin Resorts will get you there, too, but you'll have to walk a bit to get over to the BoardWalk.)
Take a look at the map embedded in the BoardWalk link above, then zoom in for an overview of the area; you'll see that transportation is easy to navigate once you think of getting yourselves to a location that has direct access to your intended destination.
Send more questions as you think of them, too, Miranda! We love to help!