I stole $900 from my manager's bank account using their login credentials three years ago. I sent an apology letter yesterday. Can I be charged?

Yes, it's possible that could be used as an admission on your part. Never feel obligated to provide a statement of this nature, especially without conferring with a lawyer first.  Should the old manager, or a police officer wish to speak further with you about it, politely decline and call an attorney immediately. 

 Yes, you could be charged with several criminal offenses. If anyone (other than an attorney with whom you may decide to consult) tries to talk to you about the matter, I recommend you remain silent (even if the person who wants to talk to you is a law enforcement officer).  You are not under any obligation to talk to, or discuss the matter with, anyone.  If anyone says they are trying to help you - or it will be better for your if you talk to them, I recommend politely telling them you need a short time to think about it -- and then immediately contact a criminal defense lawyer before talking to anyone.  Even if a law enforcement officer tells you that he can arrest you - that he won't if you talk to him, it may be a trick -- and he may arrest you later (it could be a day or months later) after he gets information from you.  So I still urge you to remain silent until after you consult with a criminal defense lawyer.