How can I say "bimestre" in English?

In Panama the schoool year is divided in four 2 month periods, each period is called a “bimestre”. What is the English word for Spanish “bimestre”?.

semester

No, that’s wrong.

quarter

In British schools the school year is divided into terms. Traditionally, there are three terms in a year, though a few areas of the country now have four-term academic years.
Many universities and other higher/further education establishments have adopted the American system of semesters instead of terms.