What kind of Disney offer are you referring to? I don't know that Disney offers any kind of San Diego Zoo/WAP ticket other than the So Cal CityPass - and that certainly doesn't include transportation to any of the parks - you have to get there yourself.
The Zoo and the WAP are located ~40 minutes apart, so they are not close together at all. Separate admission is required for both. It's not really practical to try to do them on the same day - you'd end up missing a lot. If you can only do one, I'd recommend the Zoo - I think it's a more interesting variety of animals (including the pandas, koalas, and polar bears), and it's not quite so spread out so there's less walking. Depending on the time of year you go, the weather is probably a LOT better at the Zoo, too - it's closer to the coast so it's not as warm, whereas the WAP gets really hot (90s-100s) in the summer.