Probably from Viatrix, a feminine form of the Late Latin name Viator which meant "voyager, traveller". It was a common name amongst early Christians, and the spelling was altered by association with Latin beatus "blessed". Viatrix or Beatrix was a 4th-century saint who was strangled to death during the persecutions of Diocletian.
In England the name became rare after the Middle Ages, but it was revived in the 19th century, more commonly in the spelling Beatrice. Famous bearers include the British author and illustrator Beatrix Potter (1866-1943), the creator of Peter Rabbit, and Queen Beatrix of the Netherlands (1938-).