What time of the day? AK closes early so there may not be bus transportation later in the evening. Also, be forewarned that AK busses also stop at at BB, making for a longer bus ride than most people anticipate.
No buses going from resorts to TTC...and why do you say it's a pit? It's a parking lot, basically.
I would head to an open park....DHS is a good choice if it's open..then take their bus to AKL. But any open park is a good shot. I would do that before heading to DTD and transferring...that can take a lot longer. Unless you want to hang out at DTD for a bit.