Since you are apparently under age 59½, the Form 1099-R is correct. The bank is also correct in stating that it is your own responsibility to determine the taxable amount of the distribution (with TurboTax's help). It's impossible for any Roth IRA custodian to determine the taxable amount of this distribution because it depends on information that they have no way of knowing.
Enter the Form 1099-R as received and answer the follow-up questions. Click the Continue button on the Your 1099-R Entries page, then answer the additional questions regarding your basis in Roth IRA contributions and Roth conversions. TurboTax will then prepare the required Form 8606 Part III to calculate the taxable amount of this nonqualified distribution.