You had better chances of ingesting rohypnol (the date rape drug) during your visit to the bathroom than HIV-infected blood. Besides, HIV isn't transmitted through food or drink. It's the human immunodeficiency virus, not the vodka immunodeficiency virus.
Seek some counseling or social support (or an HIV test if you're that worried...if they even let you take one) if you can't get past this issue. Good luck and keep us posted.