I'm a Bulgarian citizen. Can I apply for a Russian visa in the embassy in Berlin?

Probably. It's slightly tricky, as since the start of 2008:

some Russian consulates around the world started to implement a new requirement that foreigners can apply for a visa only at the Russian consulate in their country of citizenship or where they have residency. In fact most Russian consulates are not enforcing this, so simply check in advance to insure that you are eligible in the country you where you plan to apply.

However, that line 'where they have residency' is interesting, because if you have a residency permit longer than 90 days, it counts, and as a member of an EU state, you have a 'residency' permit for any other EU member state.

So, as quoted on waytorussia.net

This means that if you come from an EU country, you can apply for a Russian visa in any other EU country, because you are entitled to permanent residence in any of these countries by European law.

It's best to call the embassy in Berlin first though, to confirm that this is still valid and that they will be able to process this for you. There's often a bit of other paperwork as well, including an invitation to Russia which you usually need to obtain (there are companies online who will send you one), so you'll want to find that out well in advance.