The goal for a BP is about 60% humidity. However, although here in the USA, especially in the winter, many parts of the country suffer dry spells and BP's can get RI's, they can get those from humidity that is too high as well.
I would say a safe range (with ups and downs during the year) is 50%-70%. 80-87% for a day or two in shed might be okay, but not all summer. That's too high.
You will want air movement and/or a heating element that drys things out. I would also recommend paper as substrate when humidity gets high as it doesn't retain much of the humidity.