Bullock, 45, adopted the little boy, called Louis, three months ago. She and husband Jesse James, 41, began the adoption process four years ago and decided to keep the news to themselves until after the Academy Awards.
But they split in March after James was accused of having an affair. Bullock said she had begun divorce proceedings.
‘Sad and scared’
Bullock is pictured with the three-and-a-half-month baby, who was born in New Orleans, on the cover of the latest issue of People magazine, in the US.
In an exclusive interview, Bullock said she was adopting Louis as a single parent following the breakdown of her marriage, and revealed she was filing for divorce.
Speaking about her divorce proceedings, Bullock said: "I’m sad and I am scared."
Sandra Bullock on children
Reports of James’s affair with a tattoo model surfaced just days after Bullock won her best actress Oscar for The Blind Side on 7 March.
In a statement, the reality TV star later apologised saying he was "truly very sorry for the grief" he had caused his wife and family.
But he added that "the vast majority" of the allegations reported were "untrue and unfounded".
He later sought professional help to "deal with personal issues",
The edition of People magazine is published in the US on Friday