Definitely, don't put wet weed in a paper bag where there is no real humidity differential (where the outer air is also humid/wet)! At that humidity, I presume you need constant air flow, constant minimal drying on the surface, to prevent mold from taking over.
If you're going to use paper bags, you need to lower the room/tent humidity. Air conditioners and dehumidifiers are obvious options.
Sealing it up with desiccant combined with close monitoring with hygrometers is another good option (after basic room climate control).
If things go bad, if mold starts, and you don't want to try to avoid chemicals, you might try using a hair dryer to just warm and dry (partially sterilize) the surface of buds enough to stop any spread. If human hair and skin can easily tolerate a hair drier, not get dried out, much larger harvested buds surely can (and the wimpy heating of a hair drier is not going to melt any trichomes or otherwise degrade the buds). Just don't overdo it.
Otherwise, longer-term heated air flowing over the buds, such as a space heater, will also dry them, but that's could be more risky.