Bolin and Asami met through the former's brother Mako. Mako was actually dating Asami at the time. Bolin was excited when Asami convinced her father Hiroshi to sponsor the Fire Ferrets. After the attack on the pro-bending arena, Asami allowed Bolin and Mako to go live with her. When Korra was kidnapped and Asami was worried about Mako having feelings for Korra, Bolin tried to assure her that there was nothing between them but accidentally told her about the kiss.
In the final battle for Republic City, Bolin and Asami were paired up in the same group along with General Iroh. Asami's father Hiroshi had been revealed to be an Equalist. They were caught in a electric fence and thrown in prison. Hiroshi tried to get Asami to join him and they eventually escaped thanks to Naga. Eventually, Asami and Hiroshi were battling with mecha tanks and Asami was about to be crushed. Bolin came in and saved her by launching boulders at Hiroshi. He yelled at Hiroshi for being a horrible father to Asami. This allowed Asami to topple the tank over and she agreed with Bolin that he was a horrible father.
Six months, later, Bolin joined Asami when meeting with Varrick in the South Pole. Asami went to see him in order to get Future Industries back on track. Asami had initially asked Bolin to be quiet but he accidentally pointed out that Varrick was not levitating when he thought he was. However, he ended up liking Bolin's style and this eventually led to him striking a deal with Asami. Asami got happy and hugged Bolin for this. Bolin briefly ended up dating Eska, and when she demanded that he bow to her, Asami protested and told Bolin not to allow her to treat him like that.
When the rebels from the Southern Water Tribe were on trial, Varrick gave Bolin money to bribe people. He and Asami sat together at the trial. Bolin gave the money to random people which caused Asami to face palm. A week after Mako and Korra broke up, Bolin noticed tension between the two and complained that Korra had just left. Later, Mako was imprisoned and Bolin was feeling sad. Asami joined him outside to talk to him. Later, Bolin fought off a bunch of waterbenders who were attempting to kidnap President Raiko. Asami cheered once she saw Bolin defeat them.
Bolin and Asami continued to grow close together during the rebuilding of the Air Nation and the Red Lotus crisis. Bolin and Asami ended up playing a game of Pai Sho while at the Misty Palms Inn. Asami said that she would destroy him. They were playfully competitive and while Asami won most games, Bolin was about to win when Pabu jumped on the board. Later, both were kidnapped by different groups but eventually returned to the Misty Palms Oasis. Bolin immediately ran up to Asami and gave her a huge hug while lifting her up.
The Bosami ship surfaced while Book One was airing. It was mainly shipped by Makorra fans to solve the issue of Bolin and Asami being in a relationship. It is also shipped by fans who want the four members of Team Avatar to be together. Some also believed that that Bolin and Asami were both great and deserved each other. Eventually, a screen shot of Bolin and Asami sitting outside of the pro-bending arena was released and many fans hoped that it would be romantic since they were reminded of one the first Makorra moments in the same area. However, their relationship never turned romantic. Bosami primarily rivals the Masami, Borra, Korrasami, and Boleska ships.