There are 4 ways to get from Earth to Asgard, that we've seen so far:
- The shortcuts between realms. We see Loki use one of these in Thor: The Dark World. Since this relies on the presence of the Rainbow Bridge material, it's unlikely that Hulk would use this. He'd need to either purposefully or accidentally use Rainbow Bridge material on Earth. Since we don't know that Bruce Banner is knowledgeable on Asgardian intergalactic travel, it seems unlikely he'd purposefully use the stuff. And since we've never seen natural deposits of Rainbow Bridge material on Earth, it's unlikely he'd stumble upon some.
- Regular intergalactic technology, from Guardians of the Galaxy. Peter Quill was taken by the Ravagers from Earth to the galaxy we see in Guardians of the Galaxy, which indicates intergalactic travel via technology is available to the Ravagers. But we've seen no indication that Bruce Banner has knowledge or access to this technology.
- The Bifrost, from the Thor films. This would be the likely way for him to get from Earth to Asgard, assuming that's where he is in Thor: Ragnarok. It's the only method he's known to have access to, but it's not something that meets the specifications of the question, as it's not something the Hulk would just achieve by flying around in the jet.
- Dark Energy, which is another Asgardian technology/magic. This has the same issues as #1, as Banner likely lacks the knowledge and technology available to Odin. (thanks CBredlow)
It's worth mentioning that Joss Whedon originally wanted to include a shot in Avengers: Age of Ultron showing Hulk flying off into the upper atmosphere, but was forbidden from doing this. This means that at the time of Age of Ultron, Marvel did not want to show the Hulk just flying off-world, which suggests that this is not going to be how Hulk would get to another realm in Thor: Ragnarok.