Should I check "I converted some or all of it to a Roth IRA" or "I didn't rollover or convert this money"? ... for separate 1099-r just for tax submitted for me by bank?

If you have an amount in box 1 on the 1099 form that shows the tax withheld, then you can indicate that you did something else with those funds, that they were not rolled over, when asked in TurboTax. Since the funds were paid in for taxes, that is considered a distribution to you.

For the Form 1099-R reporting the amount that was moved to the Roth IRA, indicate that you converted all of the money to Roth.

For the Form 1099-R that reports the portion withheld for taxes, indicate that you did not roll over or convert this money.  You cashed it out.