Please try the following:
- Fully exit from Bushido Bear as described here: https://spryfox.zendesk.com/hc/en-us/articles/218505778
- Open your Settings app, find the Game Center option, and sign in there. If you were already signed in, click your email address once and choose to sign out, then sign in again.
- Launch Bushido Bear. Make sure to hold your device in Landscape orientation for the remainder of these steps--this will help you to avoid an orientation bug present in some versions of the game.
- A native Game Center sign-in screen may pop up. If it does, use it to sign in. Don't cancel this sign-in; if you do, it won't pop up again until you relaunch the app.
- Open the Options menu (from the main menu, click the gear icon in the upper-left corner). If the Game Center button in the Options menu says "Signed out", click it to sign in.