Research suggests that the risk of HIV infection in this way is extremely small. A very small number of people - usually in a healthcare setting - have become infected with HIV as a result of blood splashes in the eye.
Blood in the mouth carries an even lower risk. The lining of the mouth is very protective, so the only way HIV could enter the bloodstream would be if the person had a cut, open sore or area of inflammation somewhere in their mouth or throat (if the blood was swallowed). Even then, the person would have to get a fairly significant quantity of fresh blood (i.e. an amount that can be clearly seen or tasted) directly into the region of the cut or sore for there to be a risk. HIV is diluted by saliva and easily killed by stomach acid once the blood is swallowed.