BatCat

BatCat is the het ship between Bruce Wayne and Selina Kyle from the DC Comics and Gotham fandoms.

Batman 66
In "Batman Vs. Two Face", Batman is visiting Catwoman in her cell and reading her poetry. It is stated he has been doing this for a while and he admits she is never far from his thoughts and he eagerly awaits for her sentence to be up. Months later, when Batman has to skip out on his visit to her, she gets annoyed and breaks out. Later, when Two Face is auctioning a captured Batman and Robin to supervillains, Catwoman steps in and helps fight them off. Batman thanks her for helping them and asks her to turn herself in. After Batman deals with Two Face, Commissioner Gordon tells him that Catwoman never turned herself in and while he's frustrated at the news, he is still grateful for her help. At the end of the movie, Batman is being auctioned off for a date and Catwoman is there biding at the auction, which Batman blushes at.

Batman: The Telltale Series
In "Episode 1: Realm of Shadows", Bruce and Selina first meet in costume when Selina is robbing the mayor's office. After Batman deals with some goons, he gives chase to Catwoman who stole a data drive. Batman manages to retrieve the drive but not before the two fight where he gives Catwoman a black eye. After he stuns her, he is forced to catch her when she is falling from the building and when she comes to she uses the opportunity to scratch him and use one of his grappling guns to escape.

Later, when Bruce goes to talk to Harvey about the police plundering his house, Selina is there and they recognize each other (Bruce recognizes her because of her black eye and Selina recognizes him because of the scratch marks on his cheek). They speak obtusely about each other until Harvey steps away to use the phone, then start grilling each other with questions. If you have Bruce ask about her relationship with Harvey, she says she's just toying with him and if you have Bruce apologize for the black she'll say it isn't the first time she was hit by a man, which Bruce will also express sympathies for. Whether or not your forceful or softer in your dialogue, Selina gives Bruce the location of the drop off point for the data drive so Bruce can handle the people who hired her.

In "Episode 2: Children of Arkham", Bruce learns that Penguin plans to kill Selina for failing to hold up her end of the bargain so Bruce goes to help her. While speaking with her at the Stacked Deck, if you say the option "We'll fight this together", Bruce will say that he'll help her and that he's not going anywhere and if you say "I need your help" Bruce will instead say "I need you Selina". Regardless of what you say, Penguins thugs show up for Selina and she and Bruce beat them senseless.

Fanon
BatCat is one of the oldest, longest lasting, and widest spanning ships in DC Comics. While Bruce has had many love interests over the years none of them has stuck around as long as Selina has. The ship sailed in modern comics primarily due to the story Batman: Hush bring attention to the pairing once again after years of shifting popularity. While they did break up at the end that story, the pairing remained extremely popular up till the New 52 reboot and even continuing into the New 52 as they were depicted as on again off again lovers. The pairs popularity soared once more after they began dating again in DC Rebirth which lead to many fans being angered when the wedding was called off in Batman Vol 3 #50 (although it was been alleviated somewhat when they got back together). It is primarily rivaled by Superbat and WonderBat. The pairing has 2110 fanfics on AO3.

Fandom
FAN FICTION

Trivia

 * Bruce Wayne first appeared in Detective Comics #27 in March 30, 1939 while Selina Kyle appeared one year later in the very first issue of Batman.
 * In Batman: The Telltale Series 89.8% of players choose to have sex with Selina.