At first blush, I thought bi-monogamy is just monogamy, but with either sex.
In other words, if I meet a man, I will just be with that man (no other men or women). If I meet a woman, I`ll just be with that woman (no other women or men).
I thought it was a reaction to the idea that all bisexual people are non-monogamous. Which, does not appear to be the case.
I happen to be bi-curious and poly, but I`ve seen accounts of bisexuals who are pretty adamant about being with one person and one person only, and ignore the other sex while being with that person.