From what I've seen, there are two main theories about the Hulkbuster armor. The first states that Ultron has uploaded himself into Iron Man's computer systems, giving him control over all the suits. The second says that the Hulk has lost control and is rampaging through the streets. Prepared for this situation, Tony Stark breaks out the armor and tries to corral the beast. Realizing how terrible the Hulk is, he's exiled to space, setting up Planet Hulk and World War Hulk films. Now, I'm going to do something that's never been done before between comic book fans: I'm going to agree with both of you.
Tony Stark is going to need the most powerful armor he can build if he's going to fight Ultron. There's nothing stronger than a suit that can go toe-to-toe with the Hulk. So, he dons the Hulkbuster armor and heads into battle.
However, Ultron is able to hack into his computer systems and take control of the suit. He knows he will need it to defeat an indestructible Hulk. With Ultron in charge but Tony Stark still inside, the armor faces off against the Hulk. Iron Man explains to the Hulk what's going on, but the Hulk needs to defend himself. For the majority of the fight, it seems like Bruce Banner is in complete control of the Hulk, and he makes an obvious effort to not hurt Iron Man. But in a moment of extreme rage, he loses control. The armor can no longer stand Hulk's increasing strength, he tears it apart, and Iron Man is killed (cue the "but Robert Downey Junior has one more movie on his contract" and "but Iron Man is their most successful franchise" comments).
This is where things get really improbable. After the battle with Ultron, if anything in a post-credits scene, Captain America heads to a secret meeting. Here, we get our first glimpses of Doctor Strange, Black Panther, and Black Bolt. These three, along with Captain America and Iron Man, formed the MCU's Illuminati (the original Illuminati also had Namor, Mr. Fantastic, and Professor X, but those characters don't exist in the MCU, and can't be used). They group unanimously agrees that something has to be done about the Hulk.
The Illuminati reveals an early plan of Tony Stark's that involved launching the Hulk into space where he can't harm anyone. The spaceship needed to carry out this plan was already built as a precaution, and is ready to be deployed.
So this sets up Hulk's next solo outing, Planet Hulk, and his eventual vengeful return to Earth in World War Hulk. It also establishes the existence of Doctor Strange, Black Panther, and Black Bolt and the Inhumans. I know it all seems unlikely, so I do expect the usual "that's dumb" or "that would never happen" remarks, but if you have any input, leave it in the comments below!