Instead of taking the wood from the heartwood, get a piece around 6ft long with the bark still on. This will be the back of the bow. The other side that was facing inside the tree will be the belly. Cut only on the belly side to make it about 2 inches thick. Carefully remove the bark without cutting into the wood underneath. That is now the back of the bow and it shold not be thinned down any more except for light sanding to smooth. Thin the bow slowly from the belly side only. Take off a little, see if it will bend, repeat. The reason your bows are breaking is either the wood is rotten, you cut through the wood on the back, you stressed it to much too soon or the design was the wrong type for the bow/ wood you are making.
That is a very abbreviated start. Dont worry about breaking your first bows, it may take a dozen till you get it right! Just keep it up and try not to get discouraged.