Bleeding in the mouth will only invalidate the fast if one swallows saliva when the majority of the saliva is reddish.
One is not required to check the saliva to see whether it is red or not, and there is no reason to assume blood has been swallowed unless one is certain that it happened.
[Ibn `Abidin, Radd al-Muhtar; Zayla`i, Hadiyat al-Sa’luk]