(das) Zimmer is a neuter noun, the form of the neuter possessive pronoun in nominative is unser.

See https://en.wiktionary.org/wiki/unser#Inflection .

This sentence does not contain the word wir.

The subject is unser Schlafzimmer "our bedroom", which is one object, so the verb takes the third person singular form ist.

(Compare English, where "we" takes "are", but you would not say "our bedroom are" or "bedroom we are" or "we bedroom are".)