I strikes me that inspite of Bedivere's handicap, he is still accurate with his spear throwing, is favored by the king and given tasks by Arthur because he is capable, willing and faithful. He must have been a very determined man to not be detered by missing his right hand, and what a thing to have survived that loss in the first place without modern medical attention.
He stubbornly follows Arthur, and yet he is also a leader in his own right, and I think that Arthur realised how lucky he was to have someone like Bedivere as a companion.
Both Bedivere and Kay are given provinces to govern for Arthur, and I see this meeting as a high-powered conference, putting forward ideas, discussing what would work better, how to further Arthur's vision, working together to protect the land and it's people and make it prosper. Neither of them are put off by such a large task, they know they have each other as back-up and the authority of the king to handle whatever obstacles and responsibilities are presented to them.