CDing doesn't really enter into this at all, in my opinion.
I'm bisexual. You don't have to be non-monogamous because you are bisexual. It just means you can be attracted to either sex - you care about the person, rather than their gender.
There is nothing particularly special about bisexuals wanting more than one partner in my opinion - plenty of heterosexuals end up having sex with more than one partner. (Both sexes do it - but I think it's more prevalent amongst men.)
People who want to have an intimate relationship with more than one person have to have really great communications with all of their partners, and for this to have any chance of working, all parties have to be completely and rigorously honest about what's going on in the relationship, limits, if any, who are the primary parties in the relationship, etc. This is not for everyone! In fact, I'd bet that doing this isn't for most people!
Secrets, sneaking around, not telling one or more people involved in the relationships will generally destroy them pretty quickly. (How many happy secret affairs have you really ever heard of.)
I am involved in an open relationship with more than one person. I'm happy to discuss it via PM's, if you are interested. I'm not sure the site's mods will let me discuss how it works for us openly. I'm also not sure I want to discuss this openly here, quite frankly.
The short version, though, is that both you and your spouse will have to agree to one or both of you being in an open relationship.
If you find you are attracted to the same sex, while also being attracted to your wife, and she is not willing to allow any opening of the relationship, my best advice would be to love the one you are with - i.e. her. (And if that isn't possible, break up - either one is a much better option than sneaking around, imo.)
