Kurumi first sought out Shido in order to consume him and gain the mana of the three spirits he had sealed up to that point. When he attempted to seal her like the previous spirits, she played along, before trying to make it clear that she could not be saved. She is very teasing and flirty towards him especially in regards to the time he was forced to dress up as a woman named Shiori. After Shido nearly gave his life to defend her from Kotori, she appears to have become more affectionate of him to the point where, at least for now, she has made no further attempts to consume him. She has offered him her help on occasion, but made it clear that she had her own reasons for helping.
Shido's kindness towards Kurumi has proven to be beneficial to both her and everyone around her as they are no longer in constant danger; a major sign of her goodwill was shown at the end of Volume 6, where she offered Shido help to rescue Tohka. Interestingly, she seems to enjoy teasing Shido—aside from her heavily hinted feelings towards him, which is the reason why she hasn't devoured him yet, even when doing so would allow her to accomplish her goals near-instantly.
In Kurumi's eyes, the AST is no threat to her. She has allowed Mana to kill her clones in the past pretty much just to mess with her and then later appears again someplace else. Furthermore, she doesn't hesitate to pin Origami to a wall and note her intent to eat her despite how powerful a wizard the latter is. However, she acknowledges Mana's abilities to a point, noting that Shido would be safe with Mana protecting him in her stead during their assault on D.E.M.'s Japanese HQ. Funny enough, Kurumi admits to liking killing others but also liking being killed by them(her clones experience is hinted to translate back to her), so it can be inferred that she has only been killed by Mana in the past because she let her kill her, this is proven more than true when she effortlessly defeats Mana in the first battle where the real Kurumi was even present.
After her encounter with Shido, Kurumi dedicated the majority of her effort to finding Nia, the Second Spirit, so that she may obtain information about the First Spirit. To that end, she agreed to help Shido in saving Tohka from DEM because she wanted to find Nia, who was captured by DEM at the time. After finally finding her, Kurumi requested information about the First Spirit, which Nia complied with out gratitude for Kurumi ensuring that there wasn't an DEM escort when she was being transported to Japan.
The current details of their relationship is unknown for now. However, it was <Phantom> who told Kurumi about Shido's existence and powers, motivating her to transfer into Shido's class. In Volume 4, Phantom approached her about how it went with Shido. Then, she questioned Kurumi on what she wanted to use the 12th bullet for. When <Phantom> found out it was to kill the First Spirit, she mocked Kurumi for being "surprisingly gentle". Kurumi responded violently to the taunt and tried to shoot Phantom, but failed.
Other than that mocking reply, <Phantom> has made no further comments towards Kurumi's goal. How she truly feels about Kurumi's motivation of killing the First Spirit is unknown at the moment.
There also seems to be things that <Phantom> wants to keep hidden from Kurumi, as she cited Kurumi's eavesdropping as one of the reasons why she couldn't tell Shido about his past.