I had trouble finding a plastic bin that was anywhere near the right size, so I custom built a box out of okume thin plywood, just a tad smaller than the footprint of the swing out base, and just smaller than the maximum height when it swings out. Love it and it gives maximum capacity, I put a kitchen trash bag in it, which is a little bigger than the capacity. ( It is the 13 gallon size).
Below are pictures. The dimensions are: 11 3/4" x 6 3/4" base. The height is taller near the latch and shorter in the back of the big to accommodate canting it in for closure. The height is 18" tall in the front, and 16" tall in the back.
I often put in a coffee cup to hold the bin half-open while I am preparing a meal.
It took me one afternoon to make it with a table saw, some wood glue and some screws. It came out nice.