A trust is a completely private document. You are under no obligation to show the bank your trust instrument. However, if you are changing an existing asset or account in the trust, the bank may ask to see a copy of the trust. They are only doing this to verify that the trust is properly constructed and capable of holding a title to the bank account or investment. They may also want to see the signature page of the trust or the title page (the first page of the trust), and they may wish to see the portion that designates who the trustees are (the individuals who actually hold legal title to all trust assets.)
While this is very rare, there is sill a few institutions, which ask for a copy of the entire trust document for their own private records. The Summation of Relevant Trust Provisions letter, found at the beginning of the Trustee Instruction section of your trust book, should be enough to satisfy any bank or institution, which asks for this type of documentation.