It is typical of Hawthorne that no overt criticism is made of Governor Bellingham, however, if we look carefully, we can identify more subtle ways in which Hawthorne seems to cast aspersions on the character of Governor Bellingham and point towards his hypocrisy. A key chapter to read in response this question is Chapter Seven, in which we, along with Hester and Pearl, go into the house of Governor Bellingham. The narrator describes it to us and comments on the way that it is very different from how we would have expected it to be:
It had, indeed, a very cheery aspect; the walls being overspread with a kind of stucco, in which fragments of broken glass were plentifully intermixed; so that, when the sunshine fell aslant-wise over the front of the edifice, it glittered and sparkled as if diamonds had been flung against it by the double handful. The brilliancy might have befitted Aladdin's palace rather than the mansion of a grave old Puritan ruler.
It is in this last sentence that we see the criticism of Governor Bellingham, as clearly his hypocrisy is suggested by the way in which he spares himself no comfort at all in his interior life, whilst he makes every effort to present himself as a gruff, pleasureless Puritan in his exterior life.