If I can find a savings account that doesn't earn interest and doesn't come with any sort of bonus, will my savings be tax-free?
my savings be tax-free
Savings are always tax free. Only the interest earned [if any] needs to be included as income [and combined with other ordinary income] and taxed as per tax brackets.
So if you have an account that generates no interest, there is no additional income to report or tax to pay.
So if you keep 10,000 in savings account. There is no tax on this 10,000. If it generates an interest of say USD 200 a year, then this 200 will be added to your other income and taxed at your bracket between approx. 10% - 40%; i.e. USD 20 to USD 80 in additional taxes.
Essentially one need not search for a savings account that earns 0%; unless you believe that filing taxes is more complicated that earning the additional interest.