even if there are products designed to be used directly on the snake, i would reject them all and buy none of them.
mites drown in water, especially if you break the surface tension with just a tiny tiny little bit of soap / dshwasher fluid. so you dont need to use anything on your snake that is more risky or dangerous than water.
especially not on the head, the snake will breathe it in, absolute no-no. EVEN IF (and i advise against it) use anything directly on the snake, you need to cover the head with a damp towel to ensure NOTHING of it gets into contact with the head. mites move, they are not stationary, if one is on the head, then better get it a few hours later when it is elsewhere instead of risking your snake.
provent-a-mite is not to be used on the snake, you spray it into the substrate or the paper towels, where it stays active and keeps killing mites for 30 days. and 30 days is one full life cycle of the mites. you put the snake in after it is fully dried and all fumes or smell is dissipated. that alone should kill the mites even if you do absolutely nothing with the BP and dont even give it a bath. baths are for temporary relief and to clean the snake and to drown 95% of the mites that are on the snake.
dont panic, mites wont kill your snake in a day.... overusing the wrong products on the other hand can kill a snake by poisoning.
about the head: BPs can swim and dive really well. just let them swim in the bathtub, supervised, unless the snake has a serious wobble or trouble orienting all will be fine. heck if they want they can totally outswim a human. ive seen footage of a cobra crossing a large swimming pool, damn that thing was fast.