/bɜr/

That's a vowel in there.

There are different ways people say "brrr" in English. Many of those ways have a vowel in, but not all.

Yeah, a nice example for this is "myrrh" because it's a full word, not something paralinguistic like brrr. It's one of very few examples of English words that can in certain dialects be spelled and pronounced without a traditional vowel.

Hmmm. Can be said without moving your lips or opening your mouth.

Yes, but it ends with /m/. Nasal stop consonants are articulated with an open velum, so they function as semi-vowels, as /l/ and /r/ do.

Pththth!