How to make caramel sauce that doesn't taste bitter?
I would say there are 2 problems here: the lack of water, and the constant stirring. Try adding 1/4 cup of water to the sugar - this should stop it catching and burning. 

You should avoid stirring caramelising sugar because you run the risk of flicking bits of it onto the side of the pan. These isolated bits cook faster and thus burn, then drop into the rest of the sugar. Result: bitter caramel. Stirring also promotes crystallisation, which is not what you want for a smooth sauce. 

If you have to stir it, do it slowly, carefully, and infrequently - only as much as necessary to distribute the water evenly through the sugar.

I would also use a sugar or probe thermometer to ensure you're not over-cooking the sugar - get it to 350ºF, then take it off heat. This will take 6-8 minutes, and it will be a dark amber colour. Let it stand for 1 minute before whisking in your cream (I normally gently heat the cream beforehand by the way, and add a teaspoon of sea salt to it, because salted caramel is effing gorgeous).