I received stock market bonds as my inheritance from my grandparents. My family choose to cash these bonds with the understanding that no federal estate tax was required. I just received notice however that I am receiving a K-1. Does this mean I will have to pay taxes on this money? (bonds issued in Montana - I live in Kansas)

When you inherit stocks, you do not pay any tax on inheritances. Your cost basis of the stock is the fair market value at the date of death.
If you later on sell the stocks, you must report the sale on schedule D. You may have a profit or loss depending upon you sold stocks at price higher than your cost or less than your cost. It is long term capital gain.

Yes, the estate administrator will send you form K-1. You may have to report profit or loss. Find out from the administrator you cost basis of the stocks.
Read: Your U.S. Tax Return: Tax on Inheritances