Anime Introduction.
The circumstances under which we meet Rei Hino and her subsequent transformation into Sailor Mars in the anime, for the manga version go here.
Though similar, the circumstances under which we meet Rei in the Anime are slightly different from the manga. Rei is first introduced in episode 10 'Cursed Bus: Fire Warrior Mars Appears'. Most of the changes made mostly to accommodate the changes in Rei's personality in the Anime. Please note, I am going off of a subbed version of the anime, and not the dub. While as a kid I watched the dub for my writing I've been watching streamed versions of the sub.
Similarly to the manga chapter, the anime episode starts with a chat between Queen Beryl and her minions including Jadeite. Only rather than have her explaining the Silver Imperium Crystal she merely says that after his failure Jadeite has one more chance to redeem himself. This is pretty obvious series extension, but for the sake of argument we'll say it isn't. Next is a cut scene to Ami and Usagi waiting for the bus. Naru and Usagi's unnamed (as near as I can tell) friend walk up to join Ami and Usagi telling them that once people got on this bus at six they simply vanished. After some chatter, Usagi, Naru and Unnamed decide to go to the Hikawa Shrine in Sendaizaka to get some amulets to protect them from the cursed bus. Naru mentions the 'daughter' or the shrine is said to have strong powers and is really good at fortune telling. Ami is unable to join them because she has to go to cram school.
The scene moves to the shrine where several school girls are praying for luck in love. Jadeite listens in on them as he sweeps, he appears of have gotten a job at the shrine. He mentally encourages them to pray more. The scene then shifts to Rei praying before the holy fire. She senses something evil coming. We don't get to see too much of her because the scene cuts back to the girls who were praying earlier, Rei's grandfather sidles up to them and offers them jobs as shrine maidens with an extremely creepy laugh that may or may not haunt your dreams. He does a 'special ceremony' for them flailing back and forth and praying for them. After he finishes he offers to sell them more stuff, but they giggle and run off. They are soon replaced by Usagi and co. Rei's grandfather offers them the same gig as a shrine maiden, but a miffed Rei quickly interrupts him, scolding him for flirting with the girls.
While this is going on Jadeite attacks the girls who had been earlier praying for luck. Rei senses his action and throws a paper charm at Usagi, thinking her to be the source of the evil spirit. Quickly realizing her mistake Usagi is rushed into the shrine where Rei takes care of her. Jadeite delivering some towels and water, ad Naru and Unnamed friend comment on how good looking he is. This quickly brings Usagi to.
Naru asks if Jadeiete is Rei's brother. (The blonde, blue eyed guy and the black haired brown eyed girl, again, we'll just go with it). She says he isn't, and that her grandfather hits on anyone regardless of gender, and so, when grandpa asked if Jadeite wanted to work that the shrine as a live in helper he accepted. Rei apologizes to Usagi and tells her strange things have been going on recently. That her prophecies that used to be accurate have been all haywire recently. Luna wonders briefly if Rei is the princess. This is until a woman throws open the door and demands to see the high priest.
The woman claims her daughter didn't come home after buying amulets from the shrine, and that the high priest always does a 'special ceremony' around 5:30, wondering if he is forcing people to take the 6:00 bus. Rei shouts at her not to make 'strange accusations', and that they have been doing the 5:30 ceremony for a long time. She informs the woman that the police have already been there and if she wants to report a missing person she can go to the police. Standing up and yelling not to accuse her grandfather, the woman tells Rei she is extremely rude, who yells that she is the one who is rude and kicks her out.
Luna tells Usagi she thinks something is afoot, and that she should call Ami, the pair of them go to Sendaizaka Ue, and see a bunch of girls waiting at the bus stop, all of them with Hikawa Shrine Amulets. The Red 66 bus pulls up and, perhaps the most changed thing from the manga, rather than Jadeite driving the bus it is one of his minions, a typical Sailor Moon 'monster of the day'. The girls with the Amulets get on the bus, and Ami suggests they follow. Usagi chickens out however and grabs and hold onto the bus stop post for dear life, sobbing loudly, as the bus vanishes into thin air. The girls are brought to have their energy harvested as it has been 'strengthened with prayers of love'.
During the next scene Rei feeds her crows Phobos and Deimos, while Usagi returns to the shrine. Usagi tells Rei that she saw the bus vanish and Rei accuses Usagi of thinking her grandfather is at fault. Usagi apologizes, but Rei shouts that she doesn't know anything about the girls who have vanished. Usagi says she just wanted to be friends and Rei tells her to just leave. Usagi and Luna run off, but not before Luna leaves a henshin pen for Rei to pick up. She is distracted from looking at the pen too much, however, as she realizes how many more amulets they have sold since Jadeite started working there.
Rei returns to the fire to pray, asking why the bus vanishes from in front of their shrine, Jadeite interrupts to tell her her meal is ready, but she shouts at him to leave because she cannot concentrate. Rei wonders if it is his cold eyes that has made her unable to read the fire.
The scene changes and Usagi asks Luna why she left the pen for Rei, Luna says she wants to test something, but reminds Usagi that she needs to get on the bus this time around. Usagi complains that she's scared and that Ami is late. It is then that the bus shows up. At first Usagi blatantly refuses to get on the bus but then decides if she transforms into a bus attendant everything will be fine. Luna's reaction pretty much was what mine was, eye rolling skepticism. But it gets Usagi on the bus, so I suppose we can't complain too much. After springing onto the bus Usagi sees that everyone on it is out cold, the bus leaves, before Ami has a chance to catch it.
Back at the fire again Rei asks who is the culprit of all of these bad things, and Jadeite's face finally hovers in the flames. Rei rushes off to confront him, Jadeite sends Rei into the same black hole that the buses are sent to. Usagi is tossed out of the bus around the same time that Rei lands, and the demon bus driver leaves the bus, catching Rei and holding her by the throat. Usagi transforms into Sailor Moon. The symbol of Mars glows on Rei's forehead. Usagi uses Moon Tiara Action to bind the youma and Phobos and Deimos dive bomb him so that he lets go of Rei.
Usagi makes sure that Rei is okay, and Luna tells Rei to take out the transforming pen. Promising to explain everything later Luna gets Rei to say 'Mars Power Makeup' for the first time triggering her first transformation into Sailor Mars. Initially Mars looks confused, but it doesn't take her long to get the hang of this whole burning her foes to ash thing. She uses Fire Soul for the first time without any prompting from Luna. In fact, so powerful is her fire that the dimension hole through which they entered starts to close. Ami manages to keep it open, and out of nowhere Tuxedo Kamen appears to drive the buses to safety. It's truly amazing where and when that boy can materialize. Anyways, completely untrue to her manga counterpart Rei comments on how cool Tuxedo Kamen looks.
In some magical discontinuity land, Usagi and Rei get on the bus Tuxedo Kamen is flying and he guides them back out of the dimension hole. Jadeite cursing the discovery of a new soldier, and calling them 'worthy opponents'. Tuxedo Kamen vanishes and Sailor Moon asks Sailor Mars if she likes him. Sailor Mars blushes, and says of course not, that she just wanted to thank him. Sailor Mars then asks if Usagi likes Tuxedo Kamen, stating it could be one sided, starting their infamous animosity. The episode ends with Usagi sobbing and an inset of Mars sticking out her tongue.