I agree with Alex, too, bro. But at least in the US, the land of "frivolous lawsuits for dummies", few if any schools will follow up with that type of screening policy. I got blood on my cheek once when my partner was bleeding from one of his lips during rolling.
I can either freak out and let my head spin thinking if my partner has AIDS (and curse my school cuz it doesn't implement blood tests), or... I can look at this objectively and accept that
1 - the risk is there, and that it's almost as small as getting it from kissing someone for the first time, and
2 - if I ever get something in that way, it will most likely be tuberculosis, herpes, and hepatitis rather than HIV. There are more people carrying the former than the later.
Having said that, I'm doing sport BJJ where blood is rare. I don't know how abundant accidental bleedings and cuts are while practicing striking arts, not to mention in amateur/pro bouts.
I would have to be there and be splattered in blood far more often for me to begin to worry about it.