My dentist did not wash his hands before putting on gloves. Could he have infected me?

Hi doctor,

I just went to the dentist for general cleaning. My dentist is great and very hygenic. Today when he came into the room, he washed his hands and put on gloves. Halfway through, he needed to go and check on another patient. He took his gloves off and left the room. I do not know his he needed to treat or just talk to the other patient. He came back to my room and put new gloves on but did not wash his hands and continued. He, of course, would have washed his hands in the other room. I have anxiety about my health and worry about contracting something like HIV or hepatitis. While he was cleaning my gums, there was bleeding, and I am worried that maybe there was cross-infection. Am I right thinking that it would be unlikely that he could have infected me with something like HIV or hepatitis this way?