just my thoughts. is your brother legal to own firearms? must be if you think you need a bill of sale.
you said you are giving it to him. IMO this makes it a present, and you are not selling it to him or trading for other property. persoanlly i can't see where a bill of sale is needed. he's your brother, not a stranger.
for me very close friends that i have known for many years and family members, i don't do a bill of sale. anytime i dealt with a stranger i would do one.