In the mean time you could ride with a hackamore but I think that you really need to get your horse over this whole bit thing.
Putting your arm over your horses head like this may help with how your horse keeps putting its head up into the air. I would use this in combination with putting your thumb in the corner of your horses mouth.
I wouldnt reccomend just riding in a rope halter. You could try going here: Bit-Less Riding I know this lady personally. She makes everything by hand and its really quality stuff.