My bf got hiv+ blood on his hand at work. How likely is it that HIV was transmitted to him?

Unlikely but check. Getting any type of body fluid on intact skin can cause a slight risk of transmitting the contagion but the risk is very low. If there is a cut or scrape on the skin, the risk does go up. If concerned, one can get tested and assuming it is normal, one should retest again in 6 months.
Very small chance. If the skin of the hand is completely intact with no cuts, abrasions or rashes, it is unlikely that exposure to the area would result in transmission of the virus, as long as he washed his hands thoroughly and there was no exposure to any other part of the body.