You love your wife too much to put her through that kind of stress – but you’re OK with lying to her?
Sounds like a relationship problem, not a bike/spending problem.
Be open with her, honest with eachother. If she really can’t understand or doesn’t agree with what you’re doing is there a valid reason why not e.g. can’t put food on the table for kids, etc?
If not, maybe you should both examine what issue she has with it – is it just that she doesn’t want you to have it but happily spends money on things for herself?
IME if you buy the bike and hide it from her, it’ll all come out a few years later and will further erode the basis of trust between you in your relationship.
I speak from personal experience…