Who takes care of the Squibs' education expenses in Muggle schools?

Harry Potter is set in the United Kingdom. As such "Public" and "Private" schools are the same thing (for reasons of etymology going back to them being available to any member of the Public who could afford to pay, rather than only accepting people from a certain location or whose parents were part of a specific guild), although there has been effort to rebrand both of these as "Independent Schools". What Americans would call "Public Schools" are instead "State Schools".

Independent schools make up a mere 7% of UK schools, as opposed to the USA where over 25% of schools are fee-paying.

Education at State Schools in the UK paid for by the Government (although, State Boarding Schools may charge a fee for boarding, currently anywhere up to £12,000 per year. That this cost is also covered is the only "unusual" aspect of Hogwarts' pricing). As such, there are 4 options for Squibs' education:

1. Attend a State School, (no cost, unless boarding)
2. Public school, with Scholarship or Bursary
3. Public school, No Scholarship
4. Home Schooled

From a purely statistical standpoint, the first option is most likely, in which case the British Government (Department for Education, current name of the former Ministry of Education) would pay. If the family is well-off, such as the Malfoys, they have the option to pay for a Public School education. Engaging in pure speculation, it is possible that there may be endowments and scholarship funds set up to pay for Squib Education by sympathetic members of Magical society, although no evidence either way appears in the books.

It should also be noted that Arianna Dumbledore was born in 1885, and the UK only made education compulsory for children (until age 10) in 1880, raised it to 11 in 1893 (Arianna was 8), and to 13 in 1899 (the year she died, aged 14). During these early years, it is understandable that a family with minor wealth might not trust the newly created State Schools, and opt for Private or Home Schooling instead.