Marriage might be intended to be a complete union of two souls, a perfect cooperative venture between two people each committed to the well-being of the other ... but in my experience marriage actually involves two actual human beings, with faults and foibles, idiosycracies, oddities, different strengths, different motivations ... making a marriage work is hard work for this reason.
i figure there are a few times one must tell one's spouse, 'This is how it is, deal with it." Abuse that and you abuse your spouse, but sometimes to do otherwise is accepting spouse abuse.
That said, i wouldn't waste one on a bike.
As @
jppe notes, if you are not convinced you need this bike, you cannot sell the idea that you need it.
Also ... I wouldn't (in my and Only my specific relationship) try to play or fool my spouse.
I generally have said something like, "I am planning to buy this bike." Sometimes she listens to why, sometimes not. She knows that I have a bike-buying issue, but she knows I know and I manage it without hurting us. I don't consider buying Anything big without considering the household, not just my desires.
Since you can apparently buy another bike without hurting the household, then it is simply a matter of you deciding what you really want. once you understand it, just explain it your wife honestly.
But ... that is only how I might do it ... or it might not be. I don't know you, or your wife, or your situation. What is best for you, I cannot say.