Bethlehem Olive Wood Festival in Bethlehem
No independent evidence was found for a festival specifically named Bethlehem Olive Wood Festival. Bethlehem's well-documented Olive Harvest Festival, held annually in Manger Square each October or November since at least the mid-1990s, includes olive wood handicrafts among its market goods alongside olive oil and soap, and appears to be the event this name most likely reflects.
The genuinely documented festival in Bethlehem tied to olives is the Olive Harvest Festival, held annually in Manger Square, immediately next to the Church of the Nativity, to mark the close of the region's olive harvest season.