I have legal sole parental responsibility for my 3yr old, my partner and I are getting married and he wants to adopt my child. I support this. Do I have to ask bio father to sign his rights away or do I have the right to proceed without permission from bio father?

You have to get the other bio parent to sign his rights for the adoption, or attempt to have the courts take them away. Sole responsibility is not the same as him not having rights.

Also ( not knowing where you are at) but many US states will want you married and often for at least one year for the adoption.