It would be an easy offer to take at face value, if he were any good at it.

Bruce knows that his splint isn't very good- it isn't tight enough and doesn't follow the shape of his fingers well, the support and stabilization it offers is inadequate. Riku can't yet be trusted without physical restraints and Bruce doesn't relish another sprint into the woods to keep him from recklessly endangering himself. And once Vanitas regains consciousness he'll be nursing his very first hangover. There are some things Bruce has practiced left-handed, first aid, it would seem, still needs work.

The trouble is that by either nature or nurture, Bruce is always reading into things. Trying to discern where each route and each new decision might lead, the possible outcomes branching off, the motives that propelled them to this point to begin with.

The options weigh themselves.
On the hard no end of the spectrum, Bruce is unwilling to go inside or to allow anyone else in either. He's worked too hard and sacrificed too much. He is not, as Alfred has reminded him, very good at compromise. But he can try. Bruce hesitates, visibly considers the offer. And instead of answering with any pretty turn of phrase, he lifts his arm into the space between them, carefully tugging up the sleeve. This might make someone, anyone, look more vulnerable. On another face this gesture might convey the narrowest lowering of one's defenses. It doesn't look that way on Bruce.