Of the many cops and detectives on the GCPD, Harvey Bullock is one that often gets pulled into many of the high profile cases, and as such, he often is found working in some capacity with Batman...much to his chagrin.
Harvey is one of the few who doesn't fully appreciate Batman and what he does. He believes in true police work, and do things without the mass intimidation and tricks Batman does. However, over time he has come to appreciate some of what Batman does.
Harvey's history in the GCPD is dependent on which medium he's in. Many times he's shown as dirty, but crossed over to the light because of Jim Gordon. Other times they show him as a grey copy, but one who hasn't crossed the line. Regardless, he is a good detective, and though he likely doesn't admit it, Batman respects and trusts him.