The last time we saw Hulk, he was overpowered and beaten badly by Thanos.
He doesn't reappear after the Bifrost transport to Earth and refuses to "come out" for Banner.
This is the first time Hulk has ever come up against an opponent that was stronger than him, and this has shocked him to his big green core.
Hulk seems to be afraid.
Even Banner states that Thanos, with the Power stone is already the strongest creature in the universe.
We will likely need to wait for the next Avengers movie to get confirmation but this seems to be the most likely reason based on what we know.
movies.stackexchange.com/users/34402/Dave
Definitive answer from the directors here:
Hulk doesn't want to fight for people who don't care about him.
Anthony and Joe Russo appeared on a May 6 episode of Happy Sad Confused with Josh Horowitz to talk Infinity War spoilers, and during the episode, they broke down exactly why we got a lot more Banner and a lot less Hulk in Infinity War.
Throughout the movie, Banner tries desperately to bring Hulk out, but the green guy refuses.
But it’s not because the transformation mechanism isn’t working.
“If the Hulk were to say why,” Joe Russo explained, “it’s that Banner only wants Hulk for fighting.
He’s had enough of saving Banner’s ass. ”
“People have interpreted as the Hulk’s scared,” Joe Russo mused, referring to how Thanos soundly defeated him in one-on-one combat in the film’s opening.
“But it’s really reflective of his journey from Ragnarok, that these two characters are constantly in conflict with each other over control.”
It has more to do with the internal conflict between Banner and Hulk than any bruised egos.
https://www.inverse.com/article/44602-avengers-infinity-war-hulk-bruce-banner-spoilers-transformation
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To expand on @Dave's answer , Hulk just had a downfall from hubris and isn't dealing with it too well.
Hulk is basically a big ball of emotions with the strength of a titan and the brain of a child.
His sense of self is wrapped up in being the biggest and the strongest and being invulnerable and winning fights.
He's lost fights before, to the Hulkbuster Suit and to Thor, but always after a good fight.
Thanos was different.
Thanos was almost dismissive of Hulk.
Hulk lost to Thanos badly .
Hulk does one thing well and he failed miserably at it.
This calls his entire identity into question.
Hulk's has never felt vulnerable before.
He doesn't know how to deal with it; so he's scared and hiding in his room.
movies.stackexchange.com/users/13258/Schwern
Snow answered it pretty well but Joe Russo also said one more thing: "We have to be careful with the character of Banner," Joe Russo explained. "
Because if every time he's in trouble Hulk saves him, Hulk becomes the hero and he becomes whiny.
We wanted to force Banner to be the hero."
- businessinsider
movies.stackexchange.com/users/1190/Ankit Sharma
I actually assumed it was the follow up to the Ragnarok plot point that he might not be able to turn back if he shifted then - which he did.
At the time, he thought he might not be able to turn back into Banner, but I assumed it was the consequence we never had for that in Ragnarok...
(See this article that describes this more clearly and with examples.)
movies.stackexchange.com/users/63708/bdeniker
There are two scenes in the movie where Banner calls out to Hulk and Hulk denies him. These events happens after the first Hulk fight where Loki proclaims "We have a Hulk".   One is in New York during the fight with the children of Thanos. The other is in Wakanda.  When Banner called out to Hulk, he simply responds with a curt “Nooo”. What could be the reason?
Why does Hulk act the way he does in Avengers: Infinity War?
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<plot-explanation><character><marvel-cinematic-universe><avengers-infinity-war>
movies.stackexchange.com/questions/88486
movies.stackexchange.com/users/16058/Shalini
Avengers: Infinity War. This is the first time Hulk has ever come up against an opponent that was stronger than him, and this has shocked him to his big green core.   The last time we saw Hulk, he was overpowered and beaten badly by Thanos.  
The last time we saw Hulk, he was overpowered and beaten badly by Thanos.  Hulk doesn't reappear after the Bifrost transport to Earth and refuses to "come out" for Banner. This is the first time Hulk has ever come up against an opponent that was stronger than him. Even Banner states that Thanos, with the Power stone is already the strongest creature in the universe.