I'm a Bulgarian citizen, settled down in the UK. What are my options? And do we need to get married before that?
Your options are:
Your girlfriend gets a visa in her own right to work in the UK. It has the major advantage from her point of view that if you split up, she already has a visa in her own right and can decide what to do next. You will know how feasible this is.
She can apply to join you as a spouse/partner of an EEA national who is using their free movement rights to live in the UK. You don't have to be married but it will probably help; if you are not married, she will need to show that you are in an enduring relationship like marriage. If you have just got married, she will have to convince the immigration officer that it wasn't a marriage of convenience. You probably want to do this before 29th March next year in case of a no-deal Brexit (you may both get kicked out anyway, but it will be much easier to stay than get in).
I suggest consulting a paid-for immigration lawyer. They will be able to tell you how to proceed, and how to stay legal when the Home Office takes much too long to respond.
Edit: If you were a British citizen seeking to bring a Russian partner to Britain, you would have to follow UK immigration rules. For that you would have to be earning (I think) £18,500 per year (plus some other rules). Luckily you aren't, as a Bulgarian citizen, you only have to follow the (much more generous) EU rules. This is why I say you should try and get her into the UK before 29th March; while you will probably be allowed to stay under a no-deal Brexit (although even that isn't guaranteed), you would almost certainly have to follow UK immigration rules, and might not even be able to bring her in at all.