The bridge crack itself will have zero effect on the ball performance but long term it will probably continue to break out in that area and possibly even split around the ball from that weakened point.

I plug balls up nowadays as soon as I see these bridge cracks. We drill everything with a 3/8" bridge and have had zero bridge cracks that I can recall. So I am only speaking about used balls we take in. We also ALWAYS stay at least 3/4" away from the pin, or drill them completely out. (A favorite of mine)

I would ask your driller for a discount on plugging this area so that it does not spread over time. A decent shop should work with you on the repair. Take pics and send them to Columbia with your purchase reciept showing how new it is. They may warranty it.....but I wouldn't hold my breath. Technically finger grips void a warranty....so they have lots of outs on workmanship issues.

Layout & closeup of the crack

The bridge is a 1/4" so it's not his fault? That's the best he can do? I would spend my money somewhere else...that's terrible customer service.

Either through the distributor or the ball company, it usually isn't an issue getting a new ball replaced that cracks. Regardless of if it has grips glued in or pin distance from the fingers.

The ball was not bought online.  I tried emailing Columbia this morning and have not got a response yet.

Not only is the 1/4" bridge called out in almost every warranty, but a few companies include a section about bridges weakened by insufficient lateral pitches. 

One company even specifically calls out at a specific difference between lateral pitches.

I bought a Mass Eruption 2 weeks ago.  I have only thrown about 10 shots total with it in practice, and the bridge is already cracked.  I took it took the pro-shop guy and he said the bridge is at least a 1/4 inch so it's not his fault.  Can i do anything about this?  You think Columbia will help me out at all?  If not, will it have any real effect on the ball?

FYI the size of the bridge is only one thing the driller could have done wrong; to say what he did indicates he wasn't sure what else might have gone wrong and his statement is just sheer guilt, plastered all over his face as to the possibilities. That is NOT what he should have said to a customer.

If his bits weren't sharp, it could have affected the stability of the region around the holes.
If he didn't bevel the holes, they could easily crack.
If he used too much super-glue where the inserts meets the resin, he could have damaged the resin.

While there's no evidence to his guilt, there are too many possibilities that he doesn't seem to know about OR won't admit to knowing.

In any case, that's a pretty trivial crack, but it is a crack. Personally, I have had one or two of those. Most times, they never get worse (or mine didn't). One time it did and I had my driller do just what was suggested. Remove the inserts, fill the holes with urethane plug and re-drill as original. Urethane is much more durable than resin. It cost me $15 to plug and re-drill the fingers.

I would not plug the holes, but I would insert urethane finger slugs.  Works like plug, but in my opinion, is much stonger.

The only bridges I had cracked recently were all Lane#1 balls.  I usually use a 5/16 bridge and never have problems.  Like already said, be sure you bevel the holes.  Do not leave them sharp.