He was saturating her senses, seducing her somehow.
He appears to have been a convert from Paganism to Christianity, although it was asserted in later times that his father had been a bishop. That report is probably as untrustworthy as another, that he was excommunicated from the Church for seducing a virgin.
Seducing him was something she thought would be difficult, but it was actually enjoyable.
She wondered if it was because of the thought of her seducing someone else or because of her triumph at winning his affection, even if he beat her at every other thing.
The Priestly Code 3 has a different story to Balaam, in which he advises the Midianites how they may bring disaster on Israel by seducing the people Quoted Neh.