I disagree. They do have relationship, it's similar to how Dick goes to Clark when he can't talk to Bruce about things Kara does the same with Bruce when she can't talk to things about Clark (and she should do the same with Diana but that's another rant). Of course unlike Dick and Clark their relationship is a bit strange, Bruce has some affection for her but he is somewhat tough on her and likes to test her while Kara finds Bruce a bit creepy and weird but she still likes and trusts him enough to go to him for help.
Because of the short Superman/Batman arc at the very beginning of the series?
Well mainly because of the Supergirl series and one Infinite Holiday issue.
In Supergirl #9 she goes to Batman to sell him Kryptonian tech and tells him that she needs the money, Bruce obviously thinking she has money problems tells her that if she has any money problems that he and Diana would "set money aside" for her but she doesn't want hand me downs and wants to do business with him. Also at the time Kara was having problems with Kal (because she believed she was sent to kill him and was afraid she might actually do it) and Bruce concerned asks her why she's avoiding him but she doesn't want to talk about it. The whole thing ends with Bruce offering to give her an apartment and a place to stay in Metropolis in exchange for the tech and Kara giving him a peck in the cheek. From then on they build a relationship and in Joe Kelly's run it's mostly off panel stuff, but you can tell it grows because she drops in to the Batcave without complaints (well there's one from Tim who doesn't like her using the computer) and when she's in the hospital because of Powerboy Bruce finds out about it before Clark (Lois and Clark actually find out from Bruce that she's in there).
In the Infinite Holiday Special while she's trying to find a little girl who gave Superman a Christmas card asking him to find her dad, she goes to the Batcave to look for info and Alfred is with her (and with cookies). Alfred gives her advice about the situation and before she leaves she gives him a kiss and leaves a present for Bruce.
In Supergirl #23 He gives her a soundproof lead-lined present and when she opens it there's a message that say's "mistake" then Bruce calls her and lectures her about the fact that if someone bypasses the security he has in her apartment with a present that foils her powers that she should not open it and then tells her how she should not rely on said powers. Kara is slightly freaked out because it's a weird thing to do but the fact that he took his time to do it shows that he cares for her in a weird Batman way.
In Supergirl #30 She goes to him for guidance and tells him how she feels about losing Krypton. When Bruce asks her if she's talk to Clark about it, she tells him that he wouldn't understand because he grew up in Earth and did not see his parents die and then Bruce understands her and makes a comment about losing ones parents in a violent way (Bruce saw him parents being murdered while Kara saw Krypton explode with them, I mean it's not quite the same thing but it is a similar experience).
Can't remember the issue no. but when Kara loses her powers because of Reactron's gold kryptonite and while she's falling she has a flashback of being with Batman in his cave, showing her his batarangs gadgets while he explained to her how important it was that she did not rely on her powers and how she should improvise what she had with her. Kara then uses her cape to land safely and grabs a pole that she finds and proceeds to beat the shit out of Reactron. She then tells him not to underestimate her and that she has trained with Batman and the Amazons and while she's powerless she's not defenseless.
Their relationship is mostly subtle, behind the scenes and a few moments here and there but I can assure you that it has been longer than a few minutes.