The only way to get there using Disney transportation is by bus. I would imagine any Saturday would be pretty busy, although it's possible that more locals would be at the malls taking advantage of holiday sales that weekend.
Went to DTD last Dec on Sat. the week after Thanksgiving and it was packed with people. There was almost no room to walk All you could do is just go with the flow. Took over 1/2 to 45 minutes to get from HOB to Disney store. Was told by CM that Fridays and Sat. nights DTD is filled up with locals.
As posted before the only way from Poly to DTD using Disney transportation is by bus and they are always crowded on Sat. nights anywhere in WDW. That's why we rent a car.