The Cherry MX Blues have a subtle mechanical click which isn't loud, but it's still a sound that is produced (it's quieter than the sound of bottoming out). So since it's likely that you'd be using your keyboard when she's trying to sleep, I recommend looking for a keyboard that has tactile, but non-clicky switches.
However, even a keyboard with tactile but non-clicky switches (such as the Cherry MX Browns) can still be considered a "noisy" keyboard when bottoming out. Bottoming out just means that the keycap is pressed all the way down quickly enough so that it makes a "clack" sound. With rubber dome keyboards (almost any easy-to-find keyboard), this is basically the way we have to type on them. So this means that when upgrading from a rubber dome keyboard to a mechanical keyboard, it'll be next to impossible to avoid bottoming out at first.
But fortunately, it's easy to reach a point where you stop bottoming out altogether. I've learned that the best way to accomplish this is to raise your wrists up while typing while simultaneously trying to type with a light touch. So instead of hitting the keys like we do on rubber domes, you'd work towards just light taps thereby making even less noise than you might be producing on a rubber dome keyboard. However, if your keyboard is higher than elbow height or belly button height, then this may feel uncomfortable.
But now if working towards not bottoming out doesn't sound like an option, then we would need to steer you towards a good keyboard with scissor switches. To get an idea of what that might be like, almost all laptops utilize the scissor switch technology.
Although, if you are far more interested in getting a mechanical keyboard, then check out the rubber band modification using dental bands:
I haven't tried this yet, but it's supposed to help a little bit! And it could be just enough so that your girlfriend will have no trouble sleeping.