Go through the new language pair HOWTO[1] for the Bulgarian--Russian language pair. So, whereever the HOWTO reads "English", do "Bulgarian" and wherever it reads "Serbo-Croatian" do "Russian".
To get an idea of how the monolingual dictionaries of Bulgarian and Russian might look, you can check out:

* https://apertium.svn.sourceforge.net/svnroot/apertium/trunk/apertium-mk-bg/apertium-mk-bg.bg.dix

* https://apertium.svn.sourceforge.net/svnroot/apertium/incubator/apertium-ru-uk/apertium-ru-uk.ru.dix

The bilingual dictionary has already been started here:

* https://apertium.svn.sourceforge.net/svnroot/apertium/incubator/apertium-bg-ru.bg-ru.dix

If you have any questions, mentors will be on IRC #apertium irc.freenode.net