even though I never really understood the bib part. What was that supposed to represent.
That's an open flap. IIRC, we see Kirk opening and closing the flap in TWOK. The female uniform in the picture is an example with the flap closed.
Not sure what the point is, though, when there's just more jacket underneath. Might loosen it up a bit in the neck/chest area. Also not sure offhand if all the uniforms came with this feature, or it was just there on the "hero" costume (Kirk's).