Trust Issues are certainly NOT gender specific. Nor are they more or less prevalent in str8/gay/bi individuals or couples. I will say that, as a Bi Man, the act of telling the girl Im with about my personal predilections has always been really REALLY difficult in itself.
The last 2 women I dated & told both acted cool about it. Until we argued. Then - they spread hard-to-deny lies and said things that. . .well, that fucked me up as far as "trust" is concerned. The "rumors " have had a more lasting effect. Costing me (fair-weather) friends etc.
In short: I dont think I'll ever tell another woman I date. I will NOT cheat or have bi affairs either.