Kaioh Michiru lives up to her name as the "perfect soldier."[1] She is the exact recipricol of Tsukino Usagi: elegant, graceful, talented, sophisticated; but many people think of her as cold, b*tchy, and "full of herself." Could they be more wrong? Michiru may seem a little heartless sometimes, but it only because of her dedication to her mission; she won't let anything get in her way.
In her first appearance, Michiru comes off as a bit of a loner. Her manga introduction shows her getting out of a pool in the top floor of the skyscraper. She communicates through the telephone to catch a ride in her helicopter, the Kaioh Maru. This is in contrast to Haruka's "fan-filled" break-out in the next scene. You can probably guess that she has some issues with people as she is in a very tall skyscraper away 
from the general public (I mean you can only reach her by plane or by phone!). Her first documented encounter is with Mamoru on her way to pick-up Haruka. This sense of "self-satisfaction" is also expressed in the anime, especially during Episode 106. Audience members at her concert on the trip wonder about Michiru's life and personality. One even comments that it's rumored that she "doesn't like people ... although she's very kind."[2]
If you also notice in this episode, Michiru does seem a bit "light-hearted" and friendlier. She even has a friend, Elsa Grey, and has the courage to approach a person she admires with little fear. Her words are encouraging when compared to Haruka's harsh comments. I think the anime wanted to sort of round out Michiru's personality and show that she wasn't all "cold and lonely" all the time; something big had to happen to change her personality so greatly.
Many fans do question why she seems so alone and mysterious. I know the first time I saw her, I did agree with some anti-Neptuners who thought she was "too good" to be with other people. But that, of course, is not true! Michiru's detachment from society is pushed by her duty not her conceit. When she accepted her mission as an Outer Soldier, she gave up everything: her dream, her family, her life. The silence approaches and Michiru must waste no time in order to destroy it. I believe she stays away from people because she thinks they'll interfere with her mission. Not that they'll jump in front of her and block her from killing the "Messiah of Silence" or anything, but she may develop feelings or attachments to them and stray away from her purpose. If someone she has feelings for possess a Talisman, Michiru may hesitate to take it and forget all about her duty; she doesn't want that opportunity to present itself in any way.
During Episode 102 when was targeted by the Death Busters, Michiru stayed very calm and collected knowing very well that Haruka had an attachment to Usagi. She had to keep reminding her of their mission and that this was the only way. Michiru knows it's hard, but she must try to best to keep pursuing her goal and not let anything - not even Haruka's feelings - stop her.
But there is a lower-side to her "lonesome" behavior. When she meets up with people, she doesn't quite know how to carry a conversation. She'll say what's important and what she sees/feels like but doesn't say any kind of "friendly talk." 
Most of her comments seem odd to others and sometimes makes her feel a little embarrassed herself. In her meetings with Haruka (in the anime) and Mamoru (in the manga), she tells them both what she sees inside of them and shocks them with her impressive intuition. Of course, she takes this look badly and apologizes for saying such an "odd" comment.[3]
On a lighter note, Michiru is quite intelligent and has a unbelieveable intuition; her smarts even challenge that of the "genius girl" Mizuno Ami! Michiru most prominent quality is her keen perception and emotions. It's this gift that's allowed her to find her partner, detect the presence of danger, and sense the innermost feelings of others. During her encounter with Mamoru in the manga, she notices that his eyes look noble; perhaps he "was a prince in a past lifetime."[3] I think her perception is attributed by her careful analysis of people. While she stands alone, she may spend her time watching the movements of others and studying how they are, almost like a detective or investigator.
However, Michiru is not just a "smarty-pants"; she is also very gifted in music and the arts. Her violin has been her companion for what seems to be a very long time (she had it before she met Haruka and was at a professional level then). It aides her in her battles and completing her mission. In the manga, it is a way for her to gain acceptance into the Mugen Gauken academy. But mission aside, Michiru does have a great passion for her music. She plays it with much emotion and skill and even dreams of becoming a professional violinist. Nevertheless, I always sense a sad quality in her sound. It looks to me like everytime she plays, she thinks it'll be her last time and gives it her all. You gotta admire her for sticking to her violin even through her mission.
In the anime, Michiru is given the gift of painting and artistry. Her artworks hangs in very prestigious halls and are admired by many spectators. She seems to draw things that attract her interest and pays much attention to detail. We see her first in Episode 106, a vision of Haruka covered in cloth blowd by the wind, her second depicts a city ruined by water, and her third - in Episode 107 - a "self-portrait" mermaid. I give her credit for being so talented in many fields.
Haruka and Michiru promised each other that they'll sacrifice anything to ensure the completion of their task; yet, Michiru thinks that "sacrificing your partner" is not worth the safety of world. It almost appears that she is co-dependent on Haruka and needs her for herself. The most provocative example is displayed in Episode 110 during the unveiling of 2/3 of the Talisman. Eudial has a gun pointed straight at Uranus's chest and plans to shoot, but Neptune comes after her. She runs through a 
barrage of darts striking and cutting through her skin to save her partner, even for just a second. Eudial, herself, is surprised by Michiru's perserverance and initiative but shoots her regardless. Michiru values Haruka's company much more than anything in her life; it looks like she'll give her all just to keep her safe.
What could attract her to Haruka? Perhaps she fell for her looks, her style, her strength; possibly. But most likely, she fell for her personality and charm. Haruka shows a very "people-friendly" attitude. She attracts almost everyone and knows how to "play the game." Michiru admires Haruka for her immaturity at times and playful side. She's the only one who spends her time trying to talk to her and get to know her without wanting something. Perhaps Haruka has helped her to understand her dreams and that love is possible amidst tragedy.
Michiru has many facets: the dedicated soldier, the talented artist, the infatuated lover. She is not truly cold, mean, or self-centered; rather, she keeps to herself and stays away from others because she doesn't want to interfere with the fulfillment of her destiny. How selfish could a person who devotes her life to saving everyone else's be?
1 Diving Deeper. Ganymede's Sailor Neptune Shrine.
2 Episode 106. Sailormoon Super Season. Anime.
3 Act 24. Infinity Arc. Manga.