According to the answers to the question here, the Ministry of Magic covers the cost of all magical education. In addition, Harry Potter and the Deathly Hallows mentioned that Squibs were sent to Muggle schools so that they could integrate with the people like "them". As Ron's great-aunt Auntie Muriel puts it:
Squibs were usually shipped off to Muggle schools and encouraged to integrate into the Muggle community… much kinder than trying to find them a place in the Wizarding world, where they must always be second class, but naturally Kendra Dumbledore wouldn’t have dreamed of letting her daughter go to a Muggle school ...
Harry Potter and The Deathly Hallows, Chapter 8 ("The Wedding")
So it can be concluded that Squibs had two choices for education: study in Muggle schools, or get home schooling (as was the case of Ariana Dumbledore).
Then who takes care of the expenses for the Squibs studying at private/public Muggle schools? Does the MoM play a role in funding a Squib's education?