One of the long-lasting characters in the modern Batman era deserves his own post.
"Lt." (later Sgt.) Bullock first appeared in Detective #441:
But after that July 1974 appearance, Bullock appears to have laid low, not popping up in a Batman story again until nine years later, in Batman #361 (July 1983). What happened? Well, there was a brief period in there where Archie Goodwin was editing Detective (issues 437-443, exactly corresponding to the Goodwin-Simonsen Manhunter run as the backup feature). I suspect that Schwartz consigned Bullock to the dustbin when he resumed editing Tec with #444.
In Batman #361, Commissioner Gordon mentions to Batman that he's been pressured to add an "assistant" by Mayor Hill. But he's stunned when his new aide walks through the door:
As you can probably gather from that opening "belch", Bullock is portrayed as something of a slob, a definitely uncouth character. In many ways, he seems patterned on Oscar Madison from the Odd Couple, although that would change. Another inspiration would be Fat Ollie Weeks, a recurring character in Ed McBain's 87th Precinct novels, who also was clearly the template for Detective Bunz in the Hill Street Blues TV series.
Initially, it is safe to say that Bullock and the Batman did not have a friendly relationship. At this point in the Batman series, Gordon and Batman had become pretty good friends, with Batman often referring to the Commish as "Jim". Since Bullock was portrayed in an adversarial relationship with Gordon, it's not surprising that Batman would be dismissive:
And yes, he was portrayed as a bumbling idiot:
Bullock had initially planned to testify in a case against Gordon, but after receiving an apparent threat from Batman, he admits that he might have been wrong about the Commissioner not making enough of an effort to capture a criminal who was also an old friend.
In Batman #364, Bullock pulls a little prank that nearly has disastrous consequences:
But he repents:
In his next appearance, we learn that Harvey may be a pig, but he's not a rat:
And that pretty much sets the stage for the character. Bullock has mostly been seen as a slob, a klutz, and a good cop, in roughly that order, although he's also been willing to bend the rules a little bit:
Which may be why Batman and Harvey eventually became friendlier over the years.
In later years we learned Bullock's big secret; he's a old-time film buff.