The phrase "bound to him" is correct and usable in written English.
You can use it when referring to someone whose behavior and actions are bounded or restricted by another person or thing. For example, "The King was bound to his laws, and so his subjects had to abide by them."
For the way he dribbles in tight spaces, the ball bound to him like an electron bound to an atom.
Even though he is separated from George Steinbrenner by several months and thousands of miles, Winfield acknowledged today that he remains bound to him, and to the Yankees.
Back in Pigeon Creek all those years ago, she married Jake and is still legally bound to him, since he refused to divorce her.
Kesha's contract is technically with Gottwald's label, Kemosabe, so there's some question as to whether she'll still be bound to him whether or not he's at Sony.
You pity Emma being bound to him, this guy who gets on her nerves with his small-minded, small-town life, but that's only because so much is seen through Emma's eyes.
Although John Snare has led me through thickets of contradictory evidence, I am bound to him, grateful to him, for allowing me to write about Velázquez – who would have painted him with the utmost respect.
Before we end I tell him I feel duty bound to ask him who he wants to work with next, because when the Guardian asked him the same question in 2000 he uncannily replied: Adam Sandler and Daniel Day-Lewis.
Alice acts almost as his straight man, feeding him lines that are bound to set him off.
Next Jeff lumbered out, crouching warily, the colander over his head, grunting, his arms bound to keep him from grabbing at Miranda, who tickled him provocatively with her chaste white feather and lectured him on gratitude.
Some of those countries have warded off visits by warning him that, as court members, they are legally bound to arrest him.
At that time, he experimented with collage, with neo-classicism, and with aggressive dissonance, in ways that were bound to alienate him from the Soviet authorities but which began to bring him respect in the west.
