Permethrin should not be used unless it is sprayed outside and the sprayed items given ample time to close. I edited myself above to clarify that bed frames have been sprayed with typical, common mosquito sprays, wait five to ten minutes, and then check to seek if you see bed bugs. Pilgrims should not use permethrin on bed frames or anything else in an enclosed space. Hospitaleros have been trained in how to eradicate bed bug infestations and they do not need assistance from pilgrims unless they are specifically asked to do so.
Even with mosquito spray care should be used. Some people are hyper-sensitive to all chemicals and smells and we should respect our fellow pilgrims. If you are going to use a mosquito spray use common sense and not spray just before bed time, rather use it when the room has fresh air circulation, etc. and few people around. Just when you get in would be a good time. It might be worth asking the hospitalera if it is okay to spray the bed frame; tell her that you are being very careful. If there is a problem and you are concerned, move on with a smile on your face knowing that it is not personal and you are just making a personal choice.
The tough thing about bed begs is that lack of cleanliness is not a sign of potential infection or probability of infection. They can be found in the cleaniest and the dirtiest of places. They exist and will continue to exist. Spraying the frame is not necessary, it is just being very cautious and should really be used by those who react badly to bites. Otherwise, the rest of us can buy the sheets, spray our bags, and know that tens of thousands never, ever get bit.
Michael