The Winter Soldier's little red book contains the codes to bind him to a handler, who will then gain lasting control of him (unlike Zemo, who just used the temporary codes.) Since Pierce is dead, the spot of permanent handler is now free again--and the asset decides that he never wants to belong to someone who'll use him as their killer ever again. The obvious solution: Make Steve his handler.

Bucky is happy as a clam, living with Steve and being treated with even more kindness and respect than he anticipated, but Steve is horrified when he realizes that no only does Bucky have to obey his every order and try to anticipate his wishes, it can't ever be undone...