You have to build it on the ground (or stone). You can likely just build it on the ground near the wall where your bed is. Worst case is that you have to use the hoe to raise the ground in that area, but I don't think that should be necessary.

Just make sure you protect it from weather appropriately.

This is a good video to watch for some good ideas for how to build a fireplace: https://www.youtube.com/watch?v=i5wvMTLYxWI