Please accept my condolences. I don't know where you are, but in the UK the only practicable way of finding out about your mother's bank accounts would be from the documents and records that she left - eg cheque books, bank statements, building society pass books etc.
You could look into obtaining a copy of her credit reference (from equifax). This wcan show any applications for credit. e.g. Mortgages, credit cards and bank overdrafts. Not definitive though. Hunting through paper work is likely to be the best bet. Most banks send some paperwork at least annualy so you should find out what accounts are open with time. Please accept my condolences. I understand this can be the last thing you want be thinking about at a time like this.
Chris
5W Network