Friend, u seems to be fickle minded and confused. U can't see
things clearly among you and your wife actually.
Anyway, from my point of view, have you considered, she is your
wife, u can discuss it with her, thats what husband and wife got to
communicate. Let her understand what u r thinking, let it be
financial constraint or individual needs. Compromise something
between yourselves.
To be frank, ask yourself some key questions:
1.) Do you really need the bike more? Or your wife needs the car
more?
2.) Can your financial status allow you to proceed what you're
doing?
3.) Does your wife understand what you're facing?
4.) So what if you got the bike, but end up husband and wife
relationship become like shit?
5.) Or ask yourself, issit your wife that is the problem? Coz as u
said she don't pay a single cent, does that mean she don't care
about the financial status of the family?
6.) Last, if u really wan a bike, have you thought of getting a 2nd
hand? Which is cheaper and can satisfy your bike need?
Hope these helps...