From the 2000 second edition of James Saunt's Citrus Varieties of the World: An Illustrated Guide, still my go to guide for citrus variety reference:
"The Berna (or Verna) is a late maturing Spanish variety of unknown origin, roundish-oval to oval in shape, and small to medium in size. The rind has a pebbly texture and is of good orange colour but will regreen if left on the tree too long, i.e. after May. The rind is fairly thick and the juice content only moderate, but most fruits are seedless. The flavour, although moderately sweet, lacks richness. Because its quality and size cannot match those of other late varieties, such as Navelate and Lane Late and it will not hang nearly so long on the tree as Valencia, its importance is waning fast and it is rarely planted now, although there are still and estimated 1,000 ha in production in Spain."
My guess, based on the description, is that it would not be one you enjoy. His description of the flavor lacking richness makes me think it must be a bit on the bland side.