Hulk has his own issues to deal with, namely fighting for people who don't appreciate him
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.
This started out in Thor: Ragnarok when Bruce jumped out of the ship, expecting Hulk to appear by the time he landed on the Bifrost Bridge. And he didn't - Bruce just fell flat on his face, and it took effort for Hulk to appear. He probably appeared at the start of Inifinty war because he had no other choice about it, especially after Heimdall was killed and Thor placed into mortal danger. And, as stated in comments, Hulk can't do much about ship-to-ship fighting.