You can't get there directly with Disney transportation.
You have to take a bus to one of the resorts (like Saratoga Springs or Old Key West, if you want one near DTD or AKV if you want one near AK) and then a bus (or a boat if you chose Saratoga Springs) from there to DTD.
Also, they are at opposite ends of the Disney property.
If you were driving, you could do it in 20 minutes.
With Disney transportation, having to "connect" at a resort, and potentially having to wait on both buses, I would plan for at least an hour. It could be as little as 40 minutes, but it's unlikely.
Yeah, it's about a 20-25 minute drive if you have a car. I think taking a bus to Saratoga Springs and walking would be fastest. You could also take the boat from Saratoga Springs or Old Key West. The boat from Port Orleans French Quarter or Port Orleans Riverside is also fun, but not particularly efficient. You'll want to budget 50-70 minutes probably and be happy if it only takes 40ish.