Hello Russell,
Welcome back to the Disney Parks Moms Panel! Walt Disney World Resort transportation can certainly take some of the stress out of vacationing. You can just sit back and enjoy your bus, watercraft, or monorail journey.
Disney's BoardWalk Inn is not too far from Disney's Port Orleans Resort - Riverside, however, there is no direct Disney transportation at this time. You have identified a couple options: bus from Disney's BoardWalk Inn Resort to
Disney Springs or another theme park and then grab a bus to Disney's Port Orleans Resort - Riverside.
Another option and the one I would take would be to take a boat from BoardWalk Inn to Disney's Hollywood Studios. From there you can grab a bus to Disney's Port Orleans Resort - Riverside. My family enjoys the relaxing nature of the boat ride. It also breaks up the trip a bit, so it isn't a bus followed by another bus. If you are comfortable with walking, you can also take a stroll directly to
Disney's Hollywood Studios. The walk, at a leisurely pace, takes about 30 minutes at most.
If you are crunched for time, consider a ride-sharing service. Or, for a real treat, try
Disney's Minnie Van Service! They can get you there faster than you can say supercalifragilisticexpialidocious.
See ya real soon,
Anne