Why in the world would you run the engine with the radiator cap off??? THAT'S where you loose the fluid in the first place. Your expansion container/bottle acts as a bleeder at the same time.
Fill the radiator up properly, close the cap, look that there is the correct amount of cooling fluid in the expansion bottle and go for a ride. (You may idle it with cap removed until the thermostat opens and fill to top, but do not heat the engine/system up so it steams with radiator cap off.) Come back from the ride and check the expansion bottle, because from there the system will bleed and also take coolant if needed. Open the radiator cap ONLY when the engine is truly cold if you want to check, but in all reality, you may introduce more air by just opening.
See if there is in the shop manual anywhere a "bleeder valve"; if so it should sit high. But, I don't think so, however I have never had to check into it. The rest above is just common procedure.
Hope you did not over heat-the engine and blown a head gasket. If with above procedure it still overheats and the coolant smells "gasy" then you may have a bigger problem now... so let's hope it juts low on coolant and full of air with what you did so far.