Touching dogs or their saliva does not break wudu because nothing can nullify the state of taharah except things for which there is evidence in the Shari`ah.

The basic principle is that bleeding does not break wudu. Bleeding from any part of the body other than the vagina does not invalidate one’s wudu.

It is preferable for a blood donor to do wudu after giving blood, but if he does not do wudu, it is still OK.