Cate - see if they have Nupercainal at your pharmacy/drug store. It has a numbing ingredient which really helps. It's very soothing going on.
One of our sponsors - B-Sure - also makes a great product called Bottom Balm. It's also very soothing and lasts an incredibly long time.
And if those don't help then you can try the king of skin barrier products - Ilex. It doesn't let anything through. You will need to put a bit of vaseline or other product over the top of it but it's truly at the top of the butt burn/itch heap.
Regarding a bidet - I love mine. It's also from one of our sponsors on this site - COCO Bidet. I miss it when I'm away from home. If you ever go to Japan, nearly everyone and everywhere is equiped with a bidet.
kathy