Whether the novel is set in Russia, or in the Middle Ages, or somewhere in Alpha Centauri, you are writing it in English. Whether your characters are "really" speaking Russian, Old English, or a tongue so completely different we might not even recognise it as speech, English is the language you're writing the novel in, and English is the language you're writing their dialogue in. English is the only language you can expect your readers to read. Consider, last time you went to see Romeo and Juliet in the theatre, they weren't speaking Italian there, were they?
You can think of it like this: you are not writing "what happened", but your POV character's perception of what happened. Looking at it like this, either the POV character understands what is being said, in which case it can be represented by English; or he doesn't understand what is being said, in which case
The bouncer said something in Russian, which I did not understand.
That's all there is to it. It's simple.
Having characters speak in a language that neither the POV character nor the presumed audience understand is something commonly seen in movies nowadays. Forget it. You're working in a written medium (I assume), not a visual-auditory one. In a different medium, things work differently. You wouldn't expect to do the same things with coals and with oil colours, right?
Rule established, you can play around with it of course. But you need to understand the rule first, and then be both deliberate and sparing in breaking it.
Here is an example:
They got up and withdrew quietly into the shadows, and made for the doors. [...] Even as they stepped over the threshold a single clear voice rose in song.
A Elbereth Gilthoniel,
silivren penna míriel
o menel aglar elenath!
o galadhremmin ennorath,
Fanuilos, le linnathon
nef aear, sí nef aearon!
Frodo halted for a moment, looking back. [...] He stood still enchanted, while the sweet syllables of the Elvish song fell like clear jewels of blended word and melody. ‘It is a song to Elbereth,’ said Bilbo. ‘They will sing that, and other songs of the Blessed Realm, many times tonight. Come on!’
(J.R.R. Tolkien, The Lord of the Rings, Book II, chapter 1 - Many Meetings)
Here, the POV character doesn't understand the words of the song. Nonetheless, he is affected by the musicality of the language, an effect we can all experience listening to a song in a foreign language. It is this effect that the author transmits by incorporating a short text in a language we don not understand.
A different example:
'How many are you?' Robert Jordan asked.
'We are seven and there are two women.'
'Yes. The mujer of Pablo.'
'In the cave. The girl can cook a little. I said she cooks well to please her. But mostly she helps the mujer of Pablo'
(Ernest Hemingway, For Whom the Bells Toll, chapter 2
Here the foreign word is used to emphasise the fact that a particular word does not translate perfectly into English, the shades of meaning do not have a perfect match. The bilingual POV character would thus naturally use the Spanish word even recounting the story in English. This serves to emphasise the "otherness" of the foreign culture.
Is there some such specific play for you? Then spare a thought for how to incorporate it into your story. Or do you just seek to inform the reader of an interaction between your POV character and a bouncer? Then stick to the first section.
A note on accents:
Reading long sections of phonetic accent is tiring and annoying. It also creates a significant difficulty for English-as-Second-Language readers, as words written with non-standard spelling cannot easily be checked in a dictionary. Avoid it. There is nothing at all wrong with telling, rather than showing, that a character has an accent.
As an example, d'Artagnan's Gascon accent is mentioned multiple times in The Three Musketeers and in the sequels. At least twice it is a plot point. But we are never forced to read through some attempt to represent it in writing. Either you know what a Gascon accent sounds like, in which case you don't need it on paper; or you only know it's "some accent", which is really all you need to know.
(That said, as noted in the comments, there is no reason for your bouncer to be speaking accented English in the first place.)