Catwoman
Talia al Ghul
Vicki Vale
Julie Madison
Silver St. Cloud
Sasha Bordeaux
Wonder Woman
Black Canary
Shondra Kinsolving
Katherine "Kathy" Webb-Kane
Andrea Beaumont
Vesper Fairchild
Barbara Gordon
Rachel Dawes
Other (please state)
No Poison Ivy...
Are the people who are saying Posion Ivy mentioning her because they think she's sexy/like the character? I honestly don't see how she's a good match for Bats.
True but this is comics where most woman have to be sexed up but they are more developed characters who interact better with Bats. I do like Ivy but the mast majority of her stories even the popular ones with a better "portrayal" she seems kinda flat (which is more to do with the writers and a lack of popular take on her) and the only story I can remember where Bats and Ivy flirt without her seduction plant powers was in Solo where Bats say the plants look nice to wind her up.
In most comic books Poison Ivy has appeared there is some sexual tension between her and Bruce. I think they even dated for a brief period when she became human again. Don't you know that opposites attract? The tension between them is evident even in the Gothtopia arc.
As for Batman/Poison Ivy.
There is some basis for that in canon. During her earlier appearances, part of her motivation was a lust towards Batman. Later writers would start moving her more towards being an eco-terrorist. She does try to seduce him more than once but that's not a basis for a pairing.
Alan Grant's Shadow of the Bat Annual #1: Poison Ivy Year One shows her being attracted to Batman as part of her motivation. The art was awesome but the story itself wasn't great, I would take Petty Poison over that story any day of the week.
Back on topic:
Ann Nocenti's Batman/Poison Ivy: Cast Shadows-which is actually good! And a must-read for any Poison Ivy fans-showed them having an underlying mutual sexual tension. It was one of the few stories that actually shows that Bruce and Pamela could be a couple if she would just let go of her villainous ways.
In the Knight Quest arc in Shadow of the Bat title when Bruce is searching for Shondra, there is a moment where he falls asleep and thinks about his love interests and that included Poison Ivy. He points out that Ivy never knew the difference between love and lust as one of the reasons why they can't be together. It was implied that he is attracted to Ivy in a manner that is not borne from lust. Also not knowing the difference between love and lust is a perfect description of Ivy next to 'loves plants more than humans'.
Then of course, there is the most immature example in Kevin Smith's Batman: Widening Gyre where Ivy throwing innuendos at Batman asking her to come 'plow her fields'.
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Personally, I think the Catwoman/Batman thing is terrible. I mean, how good a relation can it possibly be if one of them has to completely change what he or she is about for it even to be possible?
I don't think it can ever move beyond Ed Brubaker's 'friends with benefits' stage without drastically altering the basic character concept of one of them, like happened in the old Earth 2.
Selina Kyle serving her time, reforming, retiring and becoming a stay at home wife for Bruce? Come on, how is that still Catwoman?
My vote would absolutely be Catwoman. I do not know why, but there is something about the way that I have seen their relationship develop that just makes me feel as though these two were meant for each other in some weird, rather interesting way. She is one of the few that can keep up with Bruce Wayne.