This is the way I think I would approach it...
Thinking of the outside circle as a line, I would cast on that many stitches. You would have to figure a circumference and then figure how many stitches per inch.
I would then decide how big I want my "Pie" pieces to be, and then mark them off using markers. I would then use decreases to make them smaller. You would have to figure out the differences in the number of stitches in each section from the starting line to the inner (neck) circle.
I have a few baby dress patterns that have a similar pattern idea, if not so extensive. One is crocheted and the other knitted. The angles are slighter, but the concept is the same.
I will see if I can scan the pictures for you. They are in a few "antique" knitting folio's that I have, so I doubt you would be able to find the pattern online.
I think the whole concept of the bib you are planning, is similar to a hat. Perhaps a beret top. Where the outer circumference is much larger than the inner.
The other things to keep in mind, are the type of yarn, the size of the needles etc. The finer the yarn and the smaller the needle, the more stitches you will have in each "pie" section. The more stitches, I think the more likely it will lie flatter.
The larger the yarn and needles, the fewer decreases you will put in, and each decrease will take in more. Think of it as folding a piece of paper into a fan. The smaller the folds, the flatter the fan will be. (analogy off the top of my head there) Of course you will have to put in alot more folds than the big folds.
The two baby dresses that I mentioned have a decorative lace stitching at the "lines" between the segments. I don't know if that is something you want to integrate into the design, or if you are planning a smooth pattern-less knit.
Hmm.. I think I have exhausted my current thinking. I would be very interested in seeing what you come up with, and the end result. I may even delve into the project myself! (Though I should be finishing all the other's I already have started!!)
Good luck, and I hope some of my ramblings help you out.
Now why does it take out the extra spacing I put in to make the whole thing more legible?? That's just annoying!! :??