You better make sure it is legal first. Most states do not allow hens, bearded or not, to be shot.
I didn't think that was a true statement and it seems from the responses it is not. In Ont it is the same as most. "bearded turkey"
While the idea of not shooting hens makes sense I just apply a little probability to that. If it's less than 10% are bearded that means you will see quite a few hens in gun range before you have one with a beard. Chances are as well that a jake or tom will be at the end of your gun before this happens as well so on that rare occasion you might get the shot you aren't doing a whole lot to populations stats. Add to this as well that there are hunters who 100% choose not to shoot one and you taking one is even less of an impact.
Start factoring in percenatge of those bearded hens which would be non-brood hens and........

Ah you get the point.
I don't think it is a big deal at all in the grand scheme of things so if you want the trophy, take her!
I have never had the chance but if I did I would want a standing hen mount under my full strut gobblin tom I'm getting done. After that I would want those big nasty spurs so I could pass on one.