By BSE, I presume you mean Bovine Spongiform Encephalopathy, and by that I assume you mean prions, one of the smallest and simplest infectious agents.So does BSE have a soul?
I'd guess no, as they are merely incorrectly folded proteins, not a complete living organism. Same with viruses, which are considered to be non-living organisms But, as the status of those as non-living is debatable, thus the possibility of them having a spirit or not is debatable. It's an interesting question.