I am not, of course, a woman so perhaps it's not appropriate that I contibute, but here I go anyway!
It's difficult to answer definitively without knowing the particular woman concerned. However, if we speak entirely in generalities, I do think that the analogy that some posters have drawn between the potential for a 100% straight guy cheating and that of a bi guy cheating is imperfect. The analogy is intended to demonstrate that there is an equal potential in each case, therefore there should be no complications which marying a bi guy would present for a woman in addition to those presented by marrying a straight guy.
The reason the analogy is imperfect, and that additional complications do in fact exist, is, to my mind, this: all else being equal, if we posit an unfaithful straight man, the object of his infidelity consists in seeking from a party outside the marriage what his wife (being female) can already provide him; in contrast, the infidelity of an unfaithful bi husband is of a different character, since he seeks from a party outside the marriage what his wife (not being male) cannot provide him.
The clarification I offer is not meant to suggest anything as ludicrous as the proposition that bi men are incapable of fidelity; rather, what it shows, if it is correct, is that if the potential for infidelity exists, its materialisation poses questions of significance to the marriage which are not posed in the case of an unfaithful straight husband.
The most significant question from the wife's or potential wife's perspective is, I think, something like this: if my husband or suitor is bi, am I able to offer him in mutual love all that a wife has the power to offer as the husband's "other half", or will I always be inadequate to some extent, so that the depth and intensity of our bond become correspondingly diminished? Is there always going to be some territory of my husband's soul which remains by me unexplored, unexplorable and hence unknowable (in the carnal sense of that word)?
That is a question which is not raised in the case of a straight man simply in virtue of his sexuality as such.
But, to clarify further, in the case of a bi man, the question is only posed; nothing generally dictates how the question is to be answered. An answer will depend on all sorts of considerations, and especially on the natures and personalities of the particular individual partners themselves.
There is the single concept and institution of "marriage"; but there are many kinds of particular exemplifications of it. If you love each other, do not be afraid to establish and mould your own little principality with its own constitution and habits and mores, even as it is connected to and participates in that kingdom of marriage which makes of two separate individuals a unified bond.