How can I pay my grandmothers bills with her SSI check?

She'll need to give you Power Of Attorney. You could download a form from the Internet if she isn't able to see an attorney because she is so ill. Then, perhaps, the hospital has a Notary Public who can witness her signature. even if she's in bed. You'd need a copy for her bank in order to sign checks for her. This is important for her. I hope you can get it handled.
Carol