Since the taxable part of a Traditional IRA to Roth conversion is taxed as ordinary income at your margional tax rate, nobody that does not know ALL of your income, filing status, deductions, etc. could answer that question.   Everything on a tax return can affect the final taxable amount.

$3,000 tax on $20,000 would be about 15% which is fine if you are in the 15% tax bracket but if you have more income to enter then that will probably go up.

There is no longer a 15% tax bracket for ordinary income, so $3,000 of tax on $20,000 of ordinary income suggests that taking into account all of your other entries either a majority of the $20,000 is being taxed at 12% and the remainder is being taxed at 22%, or the increase in AGI is causing a side-effect that is increasing the tax on some other income, perhaps on some portion of long-term capital gains, or is causing a slight drop in some tax credit.