Is there an easy way of converting an existing Mercurial repository to Bazaar without losing any history? If I convert Mercurial to Subversion to Bazaar will I lose any history?
You need to use bzr-fastimport plugin. It has hg-fastexport helper to dump your Mercurial history to fastimport stream which can be imported into Bazaar branch.
The entire history should be preserved this way. There is one type of information which will be lost though: information on file copies, because bzr does not support that.
Another option is to use bzr-hg plugin which should be able to work directly with Mercurial repositories. Because you're asking for an easy way then I suggest to try bzr-hg first.