"He really believed, that were it not for the inferiority of her connections, he should be in some danger."
That is, he considers himself a man free of entering an engagement - with some restraints about connections ("Pride"...), not even about fortune.
And we see he does propose in chapter 34, without mentioning, in the reasons of his struggles, being in a way or another, previously engaged, or even feeling that his mother would have liked him to marry Miss de Burgh.
He cannot ignore his aunt's wish, as well as he knows perfectly Miss Bingley's and we can see how he manages the latter's : not really ignoring them, as he does some hints upon her arts, but really slighting them, and not telling he will never marry her; anyway, why should he have to tell it? In Regency pre-matrimonial code, he has never acted as to raise any expectation from Miss de Burgh or Miss Bingley. He thought he could have acted so with Elizabeth, and was very careful to stop and had certainly relief seeing that she did not seem to have raised them; I suppose that he believed her not to have raised them, because of a consciousness of her inferiority as to birth? I see no other explanation compatible with his confidence when he proposes.