Bonding a sick rabbit

Our Barry got seriously ill back in September and suffered from a severe head tilt which has got much better recently; he's become much more active and is able to move around almost like he used to, the only problem being stairs. I'd like to introduce him to our new boy Bertie who we found to replace Barry as Mildred's friend but I'm not sure if it's safe as Barry seems to be quite afraid of Bertie. Their three meetings so far (of which two were accidental) have shown very mixed reactions: first time Bertie chased Barry around and Barry lost some tuffs of hair, second time (when I was holding Barry) Bertie was suddenly very affectionate and almost licked Barry's eyes off his head, and third time there was chasing but no hair loss. Should I continue the bonding gradually or just leave it? Barry's really enjoying his life again but he must feel lonely on his own.