Maybe I'm wrong here but I think it would depend on the situation. Bell Services will certainly help take you and your luggage over if you have your arms full of bags. But if you check your luggage with DME, it won't arrive until several hours later. And I don't know if Bell Services would be willing or able to just cart passengers over to their room.
It may depend on how busy they are at the time. If your group is just one of many getting off of the DME bus at SSR, you'll all collectively keep the resort staff pretty busy for anywhere from several minutes to more than an hour, depending on how many people arrive at once.
Anyway, if your arms are empty or you just have a few shoulder bags from the plane, I'd just plan on walking. While the resort is more spread out than others on Disney property, it's not like you have to walk several miles to your room. Unless you have mobility issues, the most distant rooms will only be 5-6 minutes away from the Carriage House when walking at a leisurely pace. It's probably a shorter distance than walking from the main gate to Fantasyland at the Magic Kingdom.