State law has no definitions on Bowie knives, dirks, daggers, poniards, double-edged, etc.
By court case law, ANY sharpening of the swedge, false edge, spine, can be considered to make the knife double edged. If most of the second edge is sharpened, it falls into the dirk/dagger/poniard class. If just the clip/false edge is sharpened, then it is a "bowie knife". As little as a 1/2" has been used to declare a knife a "bowie knife". Sometimes, even the saw back as found on a Camillus VN era Pilot's knife, has been considered "sharpened", even though the teeth on the spine are cut perpendicular to the blade face.
As to how sharp it needs to be, that is a undefined, either by state law or by court precedence case laws. If the cop decides it's sharp, that's what the judge will take. How you "prove" it's not sharp will have to be decided by the judge.
The only clip points I carry are the Kabar shorties that mimic the USMC 1219C2s / USN MK2s. From the factory, they are not sharp enough to cut paper and if you spine-whack the clip on your arm, you won't get cut (watch the tippy end

). That's what I use as a demo of "not sharp".
I have only had 1 LEO ask if one of my knives was double edged (it had a symettrical, dagger-like shape). I told him it was not sharpened and therefore not double-edged. I asked if I could take it out, he said "yes", so I took it out and whacked the back of my arm really hard 5-6 times and said "See, it's not sharp". Then I turned it over, shaved some hair off my arm and said "This is sharp".
His reply was "Yep, definitely not sharp on both sides." with a big grin. His was sharp enough to cut packing tape but not slice paper. Then we had a 15 minute conversation on how to sharpen knives.
ETA: The above applies toTexas laws as OP and I are both from Texas. Laws, court precedences, LEOs, etc. in other states/provinces may vary. Consult your local knife law attorney for specifics. IANAL.