Hmmn...I would do the front and back as two separate pieces, and the bottom and the sides as one long piece. I would cast on, using the booga bag as a reference for size...cast on 34 stiches wide, knit for 34 rows. For the bottom and side, knit as one long piece, it should be 36 stiches (two extra for selvage since you will have to seam together), then knit for 102 stiches. The handles are just i-cord. See the pattern for the Booga Bag to get an idea of how this will work.
Very interesting bag.