I'll have the character join the mages guild, and then find a lone vampire (alive or dead already), and either get infected after killing it with fire magic / a scroll, or just by checking the body out of morbid curiosity.
My problem is finding a lone vampire, as I don't know Morrowind as well as some. I imagine I might have luck in an ancesteral tomb, and I know there is one you are sent to kill int he grazelands during the main quest, but these are further out than a run of the mill Mages asignment gone wrong.
Any suggestions?