Betty Foy's son, the "idiot boy", is not a boy in the conventional sense ("a young male"). Betty Foy uses the term probably in the second sense provided by Wiktionary:
(diminutive) A male child: a son of any age
Note that Wiktionary also provides a third sense:
(affectionate, diminutive) A male of any age, particularly one rather younger than the speaker. [from 17th c.]
Unlike C.J.Sheu's comment, I don't think the term is used in a derogatory sense. Betty Foy herself uses phrases such as "my poor dear Boy" and "my Johnny", which make a derogatory intention unlikely. Due to the fact that many of Wordsworth's poems express social concerns related to the lives of ordinary people, a derogatory intention on the poet's part also seems unlikely.
It follows from the above that we can't assume that the "boy" is a child. For this reason, when Betty Foy says, "I'm almost three-score", we should assume that this literally means she is almost sixty. This mean that her son's age may be anything between late teens and early forties.
If it seems unlikely that Johnny may be in his late teens, one should look at one of Wordsworth's other poems, Michael. Michael, the shepherd from the title's poem, is at least eighty years old (line 61):
So lived he till his eightieth year was past.
His wife is 20 years younger than him (lines 79-80):
His Helpmate was a comely matron, old—
Though younger than himself full twenty years.
And their son is eighteen years old (line 124):
And now, when Luke had reached his eighteenth year,
So Luke's mother must have been 42 when she gave birth to him. It is possible that Wordsworth runs up the age of some of the characters in his poems, but this would not explain why Luke is eighteen years old and not, e.g., twenty. For this reason, the conclusion that Betty Foy is almost sixty and Johnny between 18 and his early forties should be acceptable in the fictional world of Wordsworth's poems.