To figure out the scale of your problem, buy a humidity sensor, also known as a hygrometer, for $10 to $20 at a hardware store. If the relative humidity is above 70 percent in the bedroom (or other rooms, although obviously not the bathroom immediately after a shower!), you need to take steps to get the reading down, ideally below 60 percent. If the reading is high only in the bedroom at night, try leaving the door open. A sleeping person expires a lot of moisture during the night, and it condenses on the cold glass, creating an ideal situation for mildew to grow. Opening the door allows some of the moisture to move on to other rooms.
If the humidity is high throughout your house, try running bathroom fans longer or replacing them with ones that are more efficient, opening a window for a while each day unless it is more humid outside, and using an exhaust fan in the kitchen when you are cooking and washing dishes. If these don’t bring down the reading enough, try running a dehumidifier.
In addition, you might want to check for drafts and seal any gaps you find around the window where the mildew is showing up. Opening the shades during the day, which it sounds like you’re doing, also helps dry out the surfaces and keep mildew from growing. Opening blinds only at the top isn’t a good strategy when mildew is a problem because keeping the bottom enclosed reduces air circulation in the coldest area, where condensation and therefore mildew is most likely.
As to cleaning up the mildew, the spores are just as likely to make someone sick whether they are dead or alive. So removing the mildew by wiping it away is important from a health standpoint. But dousing the stains with bleach or other products is more of a cosmetic issue. Focusing on “killing” the mildew is pointless, because plenty of live mildew spores are always wafting about.
As to how to remove the stains in the blinds, call the manufacturer. Or call one of the well-known makers of blinds similar to yours and ask for cleaners in your area that they recommend. (The Hunter Douglas referral number is 888-501-8364.) Professional cleaners of window coverings have several effective methods that work on honeycomb shades, including injection-extraction and ultrasonic cleaning, coupled with spot treatment of especially stubborn stains. It might not be possible to remove the mildew stains entirely, however.