Bridge pins are largely a cosmetic/aethestic enhancement.
Don't get sucked into all the hype you read on guitar forums about bridge pins and the so-called "dramatic" effects they have on tone.

If you have a normal bridge plate and a non ramped/slotted bridge or bridge plate, they will have a subtle difference in tonal characteristics from one material to another. Ebony pins for instance MAY (depending how acute your hearing is) yield a "warmer" tone by softening the highs and warming the bass end response. Bone pins may be identical in what they offer tone-wise to ebony ones.

Then again whatever you THINK you're hearing as a result of swapping pins, may very well be totally psychological "because you've made a swap and therefore EXPECT to hear a difference."

If your bridge or bridge plate is ramped/slotted - meaning once the guitar is strung and tuned up to pitch you could theoretically remove the pins and it will still remain strung and playable because the ball ends of the strings will be safely 'tucked into the ramp slots - the type of bridge pin material is completely irrelevant as far as affecting any tone. In THIS respect, ivory bridge pins (regardless of the type of ivory) are entirely cosmetic. But sure, they DO look nice.

The one area that CAN offer a discernable difference in tone, is the saddle material. Bone is the swiss army knife and always gets the job done perfectly. Ivory will give you more clarity, a little less "warmth" than bone" but more harmonic spectrum and "shimmer" to the overall tone. Your mistakes will also be more noticable. :-) And of course what type and material composites of the strings you use.

The MOST IMPORTANT element concerning tone - that many seem to overlook - are your fingers and what you can "pull" out of the guitar. Don't expect the guitar to play itself nor the choice of nut, saddle, or bridge pin material to ever compensate for the person playing the instrument.