BatFamily and Their Batman Ship:
Alfred - BatCat. Even though he disaproves Selina criminal life he enjoys her company enough it doesn't really matters. He thinks Selina and Bruce are perfect for each other.
Jim Gordon - BatCat and BruHarvey before discovering that Batman and Bruce were the same people he kindda just belived Catwoman was Batman's soulmate and Harvey was Bruce's tragic soulmate. Is more inclined towards Bruharvey because he thinks Bruce is the only one who can get Harvey's back and he and Harvey really bonded working together and he saw Harvey as an younger brother before Two-Face.
Dick - BatCat or SuperBat. He loves both Clark and Selina and both were basically parents for him in a way or another. He is very disapointed in Bruce for never acting on either of his two very obvious crushes. He is even more disapointed after Khoa breaks Bruce's heart.
Dick is an anti-GhostBat and Khoa will have to do a lot of work to prove his worth to Bruce's eldest child. He also disaproves of BruHarvey.
Barbara - BruHarvey or BatCat, just like Dick she grew whatching Selina sending Bruce the heart eyes and also respecting Selina as the ultimate girlboss. But while Dick was seeing Superman sending his dad love eyes, Barbara was seeing her uncles Harvey and Bruce weirdly pinning. And while Dick and Harvey never got along at all, Harvey was very close to the Gordon family as a whole and used to babysit Babs a lot.
Jason - Brutalia and WonderBat. He accepts some of Bruce's other love interests, but he doesn't like them. Talia means to Jason the same that Selina means to Dick, she is basically his mother and he adores her.
While Jason would support Wonderbat as well is important to add that he thinks Diana could and should do better. He thinks the same of Talia, but he also knows how much she likes Bruce and believes Bruce does act better when with her. He is starting to think BruHarvey is also not that awfull of an idea.
Cassandra - She saw most of Bruce's romantic phases with people and she has no fix idea. She just wants Bruce to be happy. If she had to choose one option would probably be Talia, but in parts is because she has a tiny crush on Talia.
Tim - None. Tim doesn't think anyone is good enough for Bruce. Or better put he thinks Bruce is too emocionally fragille for a relationship. Anyone who dates Bruce will have to deal with an overprotective Tim.
He specially distrusts Selina. The closest to a Bat ship he has is BatLatern cause Tim was the Robin during the time Bruce and Hal were having the weird "chair" friendship and it kindda reminded Drake of him and Kon. Still he is very anti Batman dating and will make a PowerPoint presentation of "things I'm going to do with you if you ever hurt Bruce."
Stephanie - Thinks Bruce is too much of a loser to date. Does ship BatCat. She likes Selina and like all Robins saw her and Bruce weird flirt, she thinks they match. She also supports Brutalia, mostly because Damian convinced her. She just really doesn't care. Will write trash fic about Batman and his Rogues. When Riddler was living at her home she would specially make fun of his crush on Bruce. But is more her being a little gremlim than anything else.
Damian - Brutalia. Duh. He wants his parents to be an item and he wants it now. Will do a parent trap if necessary. Sees good points in other ships, he actually gets along well with Selina and with Clark, but I mean, he is on his mother's side.
Duke - Coudn't care less. There is only one superhero love life he cares and it's Black Lightining and only because now that his mother is unjokerized she and Jefferson are actually kindda cute together. He loves Bruce but that man's love life is just too messy for him to have an opinion on. While not as protective as Tim, Duke is still very protectice of Bruce.
Bao - GhostBat. This child of divorce just wants to see his parents get back together and he will foght the other child of divorce (Damian) over it.
[I can't imagine neither Kate nor Helena even participating of such debate because both are really not intererested in Bruce's weird love life. I also have no idea what Harper, Cullen, Maps or Luke would think].
All members of the batfam hate BatJokes.
Disclaimer: there is very specific situations with different ships, for example I personally believe that Lego Dick does shipp BatJokes and Unburied Babs ships RiddleBat. But this are very specific versions of the characthers and not the general norm.
