You understanding is right.
— Извините,— сказала я холодно и хотела высвободить руку, но кружево рукава зацепилось за его пуговицу. Он, пригнувшись ко мне грудью, стал отстегивать его, и его пальцы без перчатки тронули мою руку.
"Excuse me", I said coldly, and I wanted to free my hand, but the lace of the sleeve caught on his button. Leaning his breast towards me, he started to unfasten the lace, and his ungloved fingers touched my hand. (translation mine, Q)
Пригнувшись ко мне грудью (literally, "having leaned towards me with his breast") is a stylistically clumsy, if accurate, way of describing the posture of a man who is forced to lean towards a woman while still trying to appear keeping distance from her in a situation like this.
Out of context, this whole phrase is not what they call flawless Russian: use of отстегнуть (кружево) instead of выпутать (пуговицу); the pronoun in его пуговица; repetition of рука etc. are generally considered poor style. However, Tolstoy is actually famous for using this kind of clumsy language (often lost in translation) that, as many think, conveys conflicting feelings of his characters perfectly.