My mother sang this to me in the late forties.
She sang

Daddy turns the light off as he tucks me up in bed
And he kisses me before he goes
He says the angel keeps
His darling while she sleeps
But do you think the angel knows
That every night when daddy's gone
And slams the study door
There's a grumpy little noise upon the stair
And I shiver in my byes
As I close my sleepy eyes
In a fright
That it might be a bear.

Are you there Mr Bear
Don't you dare to bite from me
For I shall scream and very quick
My papa will fetch a stick
And he's not afraid of bears. Not he.
So if you want a little baby girl
And you're hungry and you can't wait any more
I can tell you where there's plenty
Have a try at number twenty
Go and bite the little girl next door.

Verse 2 as above.

No one ever among my friends has heard of this song. I am 73. It would be a shame if it faded away.