Are the bull's heads supposed to be kept throughout the entirety of the game? In the rules, it is written to keep the bull's heads into each subsequent round. When I play on BSW and each round starts off with a clean slate; is this just a translation problem?
From where in the rules do you get the idea that the bull's heads carry over? On my reading of the German the matter isn't actually spelled out, but the implication is that each hand/round starts with a fresh slate.
At the bottom of page 2 there is a section headed "Spielende". The three lines that follow this heading translate as, "A game section ends as soon as one player has no more cards in his hand. The other players add up the bull heads on all the cards still in their hands. These count as minus points."
There is then a two line example ("Beispiel").
This is then followed by four final lines which translate as, "The minus points are written down and the next game section begins. As many game sections are played as there are players taking part (for example, with three (players) three play sections are played). Whoever has the fewest minus points at the end is the overall winner."
There are no actual instructions on what to do at the start of the next "Spielpartie" (which translates as "game section", but which English-speaking card players would normally call "hand"), but clearly you have to start it by shuffling the cards and dealing everyone a fresh hand of 10 cards. This takes us back to the section on page 1 that is headed "Spielvorbereitung" (= "game preparation"), where this instruction is the first sentence of point one. Point three of that section tells you that "The bull cards are laid ready as a deck next to the deck of oxhead cards." In the absence of a word like "remaining" or a rule saying that players should retain any bull cards acquired in previous rounds, my assumption is that this "point three" section means "all the bull heads".
I think that this is one of those games where each hand is to be thought of as really being a complete game in itself, but you are keeping an aggregate score over a set of games.