Yes, the only way to get to the AKL from the AK using Disney transportation is to take the bus. The AKL is very close, so it will be a short ride. If you do not have a car, the only other option is a taxi.
The options for lunch at the AKl are Mara (like a food court) and JIKO (upscale, sit down restaurant). BOMA (buffet) is not open for lunch.
FWIW, I'd recommend BOMA - lots of choices for both adventurous and not-so-adventurous eaters. You could try for the earliest dinner seating (around 4 or 4:30, I think) or the latest breakfast seating (10:45 or 11).
The AKL is just beautiful - worth a trip to look around. There is an animal viewing area there just off the awesome main lobby. We saw giraffes, zebras, ostriches and some type of deer/antelope animals. The large gift shop is fun, too - lots of African items as well as the more traditional Disney items.
Enjoy your trip!