I now at the point where I think that Bismark want to be ringed as well
Nah, Bismarck just want to be praised and pampared. I don't think she has naughty intentions or even think about the ring. She's a big child, but still pure at heart. Graf is probably more worried about the fact that the admiral could land a hand on Bismarck for being too close to him, so she's hyper-worried and need to watch him constantly.
You can just see the conflict on poor Graf's face, wanting to help her sister ship, and yet...having her man encroached on, even if it's in a totally platonic(?) way.
I can only imagine the embarrassment big Akatsuki will have once she snaps out of her regression.