As short as 20 minutes and as long as an hour. If you have a golf cart and ride it to either the front or rear of FW to catch the bus, then its quicker. If you use the shuttle bus inside FW, it will take longer. You can bet when you walk to the bus stop, the bus will have just passed and you will wait 15 minutes or so for the next one. Then as you exit to transfer to the park bus, the one you want will have just left. So you wait again. Every bus to every park will come and go before that one bus you are waiting for arrives.
Or you ride the shuttle bus to the outpost and wait forever, just to find out the bus you want picks up at the other end of the park. Sometimes it pays to read the material they give you at check in.
We stayed at the fort last April for 10 days and out of the 10 days took the bus the first 4 days and then we said forget it...it will try your patiences...it took us an hour or even more everytime we took the bus with out fail and our campground was not even full. If your patience and look at the bus ride as part of the magic then you will be fine if your impatience ( like us ) it will drive you up a wall.
We waited two hours plus once while going to epcot we made a stop at Wilderness lodge and I thought I was going to lose my lunch.