If I call the credit card company to have her name taken off, how long does it take for the credit bereau to recieve the information
Possibly. Since she is an authorized user, account information for the card may also show up on her report. The good news is that it will not look as if your daughter is the one that filed for bankruptcy - the bankruptcy itself would only show on your credit report in the adverse information section (usually at the beginning of the report).
I don't know how long it would take for the credit bureaus to update changes in information. You might want to try contacting them directly with your question: Equifax 866 640-2273; Experian 800 493-1058; TransUnion 800 916-8800.
It is best to remove all authorized users from your accounts before filing for bankruptcy. It can affect your daughter's credit report. FICO has announced recently that it will no longer count authorized user accounts toward the FICO score. I do not know when this change will take place.
[This communication is intended as general information and not specific legal advice, and this communication does not create an attorney-client relationship.]