From the Global Anabaptist Mennonite Encyclopedia Online:

Bixel (Bixler, Bichsel), a Mennonite family name originating at Eggiwil in the Emmental, canton of Bern, Switzerland. The word "bichsel" was used for a rounded adze which was used to hollow out wooden troughs and spouts. It was likely that persons who made or used this tool were given this name during the 15th century. The first mention of the name in connection with the Anabaptist faith is in 1537. Ulrich Bichsel was executed at Bern with six of his brethren during the latter part of 1537 or early part of 1538. He was the 15th Bernese Anabaptist to suffer this fate. Simon Bichsel was called before the authorities in 1621 and questioned concerning his Anabaptist faith. Various officials pointed out his errors and pleaded with him to recant. He answered them by saying that all their teaching, threats, and punishment will avail nothing as it is written in the Scriptures, "Go out from them."

Andres Bichsel appears to have been the first of the family to have moved from the Emmental to the Jura. He arrived near Corgemont in 1717. During the following decade several other Bichsel families followed, most of them settling near Court on the Graitery Mountain and in the Chaluet Valley.

Probably the first of the families to migrate to America were John and Christian Bixler who settled near York and Hanover, Pennsylvania, about 1725; a third brother is said to have moved later to Virginia. In the early 19th century a branch of the family settled in western Pennsylvania near Butler (Bishop Joseph Bixler, 1778-1862), and in eastern Ohio near Columbiana (Bishop Joseph Bixler, 1813-1895). Bishop Jacob Bixler (1877-1939) of Elkhart, Indiana, was of this line. Descendants of the original immigrants in mid-20th century lived in Pennsylvania, Virginia, Ohio, Indiana, and Illinois.

Jacob Bichsel and his wife were the first of the family in the new Swiss emigration to America in the 19th century. After arriving in 1821 they settled in the newly established Sonnenberg settlement in Wayne County, Ohio, where most of their descendants lived in the 1950s. They used the name Bixler. Jacob's brother and sister, Peter and Verena, followed in 1824, settling in Holmes County, Ohio. In 1845 Peter and his family moved to the Putnam County, Ohio, settlement where most of his descendants resided in the 1950s. They used the form of the name Bixel. Some members of these families were also found in the Berne, Indiana, settlement.