It took us about 10 minutes from our room to the turnstiles last time. But it varies a bit based on where you room is located (and how fast you walk, of course.)
You only have to cross one main street - Harbor Blvd. If you go look at the map view or satellite view on google maps you can see the route pretty easily.
We go just a bit north on Harbor. Then cross Harbor at Disney Way. After that you do have to cross Disney Way but it's not bad.
There are cross walks and signals.
You can also see a street view of Habor using google maps. It's kind of fun.