I have hsv-1 what is the chance that i could transfer the virus to my bf, when i have no cold sores present?

Up to 50%: Half of all people have hsv1 by the time they go to college. So there is a 50% chance that your boyfriend already has it and there is no issue about passing it to each other. Even without an active cold sore, there is some asymptomatic shedding that occurs always, so you can pass it to him even if you don't have cold sore if he is negative for hsv1.

Not likely: You may not be aware that you have lesions present but if there are no lesions and not vesicles you are not contagioius... It is important to avoid contact with mucous membranes that are infected if lesions are present and routine hygiene like hand washing is critical.