There must be a way to turn ores into ingots right?

use the smelters. they are the big dome things usually located right outside mines or next to smithing stations

There's one in Whiterun behind the armor merchant.

If you are on PC I have a suggestion for quick smelting. First put your mouse over the ore you want to smelt. Click with your mouse and it will ask if you want to smelt. move your mouse over to hit YES (since for some reason ENTER doesn't accept it... thank you Bethesda). Now position your hands to hit Enter and Left click really fast. It will remember where your mouse position was over the ore type and you can quickly just spam through it all.