Though Governor Bellingham is a firm, unstinting upholder of law and order in the Massachusetts Bay Colony, he's also a fair man. So when Hester attempts to intercede with him to prevent Pearl being taken away from her, he hears her out.

Bellingham is as staunchly committed to the prevailing Puritan value system as anyone; but crucially, he also believes in doing things by the book. By the standards of the time, he would've been well within his rights to have ignored Hester's concerns and sent her packing with a hellfire and brimstone sermon ringing in her ears. That he chooses not to follow this course of action indicates his fidelity to the law. Above all, this means listening carefully to what Dimmesdale and Hester have to say concerning the welfare of their child before arriving at his decision.

Hester and Pearl do pay a visit to Governor Bellingham, but they do not stay with him for any length of time.  The reason for their visit is so that Hester can drop off a pair of gloves that she embroidered for him based on his specifications; this kind of work is how she maintains her home and her daughter.  When she gets the chance to speak with the governor, he is attended by a few other gentlemen of the town, including Reverend Dimmesdale and Roger Chillingworth.  Pearl's behavior alarms the governor, and he indicates that it might be best for Pearl to be taken from her mother's care and educated properly.  One older minister promises that she would be well cared for, but Hester is desperate to keep her daughter, saying that God gave the child to her, and she appeals to Dimmesdale to speak on her behalf.  The governor is convinced by Dimmesdale, and so Pearl is allowed to remain with her mother.