I have a crankbait that runs to my left when I retrieve it. I can’t bend the eye very easily so I’m going to shave down the bill on one side to straighten it out. If it runs to the left when retrieved, which side of the bill should I shave off material?

Most times its the line tie causing the problem not the bill. Always hold the bait facing you & bend the line tie left if the bait runs to the right and the opposite if its running left. A pair of small needle nose pliers should do the trick. Always bend in small increments then test the bait to see if you need more adjustment. 

It doesn't take much bend at all to fix an out of tune bait at all. More often than not you can't even tell that you bent it at all.

Don't shave the bill material.  This will permanently alter the bait's action, and usually not for the better.  Ask me how I know this, heh. Get in there with some needle nose pliers, as Dwight said, and make small adjustments.