Bruce Wayne and Batman have had many girlfriends over the years, and this post will be an effort to catalog them all. It's going to be an enormous undertaking and I invite assistance from my fellow Bat-historians.
Julie Madison: Julie was the first love interest. She did not appear in the initial four issues, but in Detective #31, she was introduced as Bruce's fiancee:
In Detective #39, Julie becomes a movie actress. Batman saves her life from a crazed old actor named Basil Karlo. And we see at the end that perhaps she is not fated to marry Bruce:
In Detective #49, Julie's name is changed by a Hollywood publicity man to Portia Storme, and she becomes a major star. Disappointed in Bruce's apparent dissolute lifestyle, she breaks it off with him:
As far as I know, Julie did not appear again in a non-reprint until the late 1970s when she popped up in an issue of World's Finest.
The next significant woman to pop up was a Batman love interest. In Batman #1, he has his first encounter with the Catwoman (in that story, known only as the Cat). She makes him an offer here:
But at the end of the story, Batman lets her escape.
I could fill pages and pages with the on-again, off-again relationship of Batman and Catwoman, so here are just some highlights. In Batman #62, we learn that the Catwoman had been a stewardess, who lost her memory in a plane crash and became a criminal. For several years after that story, she became reformed, and worked to help Batman on a few cases. It is noteworthy though, that almost from the moment she ceased being a criminal, Batman stopped expressing any romantic desire for her.
In Detective #203, Catwoman resumes her life of crime in anger after a newspaper published a story about the many times Batman defeated her. Detective #211 contains The Jungle Cat-Queen, one of the greatest Batman stories of all-time, but after that tale, the Catwoman disappeared for many years. When the Batman TV show started, she was a frequent guest villainess, although she did not reappear in the Batman comics until Batman #197, as the show was ending its run.
In the 1980s Catwoman again teamed up with Batman on several occasions, fighting crime and romancing Batman. I believe that relationship continues to date. Incidentally, the Earth II Catwoman apparently never resumed her life of crime and eventually ended up marrying Batman.
The next significant love interest was Linda Page. She was a former socialite in Bruce's circle who has gotten serious and become a nurse. In the story, her neighbor's son has fallen in with a rough crowd. Batman lends a hand and convinces the youngster to go straight. In the end, as he takes her to a restaurant she raves about the dash of Batman and makes the usual unflattering comparisons to Bruce.
In Batman #6, Batman saves Linda's father's life and his oil business. When Bruce shows up, inevitably too late, she doesn't have much time for him:
This highlights one of the problems facing Bruce in the romance department. The gals he likes are unlikely to stick with him given his supposedly dissolute lifestyle. And he's unlikely to be attracted to the ones who would be happy to party all the time.
Linda made quite a few appearances in the next couple years, but her finale came in Detective #73. After that she simply disappeared. One presumes that Bruce got tired of her constant hectoring him to make something of his life.
The final love interest of the Golden Age was Vicki Vale. Vicki was a photographer for Picture Magazine who first appeared in Batman #49. Bruce is interested right away:
One thing Bruce definitely likes about Vicki is that the moment excitement happens, she dashes off and deserts him for a photo opportunity, giving him the chance to become Batman. However, she's also too smart not to notice things:
This sets the stage for much of Vicki's Golden and Silver Age appearances. She becomes something of a secret identity pest, like Lois Lane in the Superman series. However, unlike Lois, she doesn't work alongside the man she suspects of being a superhero, and thus her appearances in the comics are much less frequent.
In Batman #79, she becomes the Bride of Batman:
It's an incredibly convoluted tale. Vicki meets a foreign potentate who is so taken with her beauty that he proposes to her on the spot. Not wanting to cause an international incident, but also not wanting to marry "that funny little man", she desperately blurts out that she's already engaged to Batman. A rival photographer, suspecting that Vicki's lying, turns the heat up by announcing a date and sending out invitations. The Shah decides to be the host and it looks like Batman will be forced to the altar to avoid diplomatic embarrassments for the US. Vicki admits to her rival that yes, it was all a ruse but now that she's got Batman trapped she's the happiest girl on Earth. But the Shah insists that the wedding be canceled when he learns that Vicki would have to undergo plastic surgery to disguise her after the wedding so criminals could not get revenge on Batman. And fortunately his custom demands that he not marry anyone previously betrothed to another.
Vicki disappeared for about five years from 1958-1963, then returned for a few appearances in the Silver Age during the latter part of the Jack Schiff era. I'll talk about those stories in an upcoming post on the Silver Age girlfriends of the Caped Crusader.