What is the Russian word that sounds like "bleen"

As another native Russian, I agree with previous contributors. You use “bleen” (блин) instead of “blyad” (блядь), if you don’t want to swear. There is nothing in common between the two words, other than the first two letters. “Bleen” is an inoffensive euphemistic substitute for “blyad”, meaning to express disappointment or frustration. It is like saying “darn” in English instead of “damn”. Or rather, saying “darn” instead of “fuck” or “shit”?

Gosh, some people say bleen when they understand that someone else can hear them and they don't want to swear aloud. But since words sound similar and bleen is just a "crêpe" / "pancake", while the other word means "slut", you kinda slide into lighter version of this sudden swearing. Bleen is allowed on TV (though not appreciated because associated with uneducated speaker) and "blyad'" is forbidden.

I would never translate "bleen" as "bloody hell" though. It's just an "oh, crap!".

Bleen (Блин) - not swear word. Translate as "Pancake". But have a second meaning - the annoyance that something did not work out

Blyat (Блядь) - Translate as "Whore". And it also has the same meaning as "Блин"

You will gain a deeper understanding of Russian swear words by trying to translate the lyrics Ленинград - Непросто

I'm native russian. I think, "bleen" is less rude word than "blyat". It sounds more like "shit", "fuck", "damn it". We use "bleen" in our informal speech, and it's OK. No one will shame you, if you use it. Another thing with "blyat". We don't use it often, especially with strangers. It's prohibited in formal communication and is considered as bad word in everyday speech. You can easily shock your friends if you use it without any emotional need, i.e. if you aren't in humor, or something really bad has happened.