Is the lack of humidity the reason why a Carbon Fiber bow might get less stretched?
I wouldn't say there is a "standard" way, but the most popular way is probably the Damp-It line of products:
The violin specific one:
The are other products from other manufacturers, usually based on the same concept:
You can see in addition to the tubular form (like the Damp-It), there are sponge-like bags that you can wet and put into the case to keep the case humidity up.
A newer concept is to use a special gel in a pack. The gel contains extra moisture that will evaporate to humidify the case, but the gel will also absorb moisture from the air if the humidity in the case is too high. Eventually the gel will either totally dry out or become waterlogged (you'd have to live in a tropical climate I expect for that to happen), and you have to throw it out and buy a new pack. So far, I have only seen this system made for guitars in the form of the Planet Waves 2-way humidipak system.
The actual carbon fiber material of the bow should be completely unaffected by humidity. It may be that the horsehair (if it's natural) may shrink or stretch with humidity and that may affect what you're seeing. Obviously a wooden bow may be more affected by humidity changes.
Remember to loosen the frog on the bow between playing to extend the life of the hairs and the bow.
Others have addressed the how-to aspect of humidifying. (On that topic I will add that a lot depends on the humidity level in your home, noting that you don't have to necessarily keep your case closed when your violin is at home. If you have electric forced air heat, the humidity will be lower in the air in your home than if you have gas heat, for example. If you have very dry air in the colder months in your home, you might want to humidify a bit, to be kind to both your string instrument and to be kind to your respiratory passages. Be careful not to overdo it though (you don't want to start growing mold on the windows). Where thermometers are sold you can buy something that measures the humidity in the air.)
But mainly I want to focus on the bow hair aspect of your question. Bow hair can indeed get floppy and this can be frustrating. I think humidity tends to make bows a little bit more on the floppy side, so make sure the air in your house isn't too damp.
It might be time to take your bow for a re-hair. A luthier who works on bows will not charge you to give you an opinion.
There remains a decent amount of controversy over how best to take care of your instrument vis a vis humidity. The ideal situation is to have a humidity-controlled room and never leave :-) , but...
I'm in the group that worries most about rapid, repeated changes in humidity which could cause stress problems. If you have a well-humidified case but then spend 4 hours rehearsing in a dry hall (can you tell I live in New England? ), then drop your violin back into the humid environment, that might be worse than just keeping the instrument dry-ish all the time.
But I do stress that there are other groups who believe strongly in humidifying the case regardless of room conditions, so YMMV.