Firstly, +1 on telling us what your other bikes are.

Other than that, it sounds like you really *want* to. If a $2700 treat is out of line, then coming up with a justification is pointless. If $2700 luxury items are in line with your family budget (you drive a Lexus instead of a Toyota), just buy her something nicer a couple months before you bring it up.

A toy is not a rational decision.

Your first decent quality bike (say, a 105 level road bike) can be construed as a fitness tool. By the time your stable hits 3 though, you're deep into hobby territory.