Bathroom bins are gross. Do you really want your relatives emptying your sanitary products?
Nobody’s expecting them to rummage through with their bare hands – you just tie up the top of the full bag and fling it in the main bin. Most rubbish is dirty and often a bit whiffy - emptying bins is just part of everyday adult life.
We didn't have a bathroom bin in the guest loo for a while. An acquaintance came from Xmas and she was in the loo for ages. After she came into the kitchen sheepishly and had to ask my DH where the bin was. He said 'oh yes hand it over and I'll put it in' and she had to declare the contents to him! I felt so bad for her and was online that night ordering a bin!
That’s the perfect way of ensuring that she will never ever want to visit again. Has your DH really never heard of the concept of periods before? Did it not occur to him that, emerging from the toilet, it might be something a little more personal than an empty crisp bag?
I grew up with a father who ridiculed periods so I would feel incredibly uncomfortable if my FIL could see my used tampon in the bin. So I’d rather be taking it home in a sanitary bag. It’s a bit gross, I know.
What a nasty, abusive man. But I think the chances of your FIL being the same are very low indeed, aren’t they? I can understand how growing up with such a frightful man would destroy your confidence, though, and make you feel shame where none should ever exist 
Eh..try this:where do you want me to put my tampons/sanatary towels?there is no bin in the bathroom.
I belief all women at some point in their life have a period, is it such a big deal to ask where to put tampons. Unbelievable prudishness!
Everybody poos as well, but I don’t think many people would want to ask their hosts as to how they can open a locked window to get rid of the stink or how they should scrub away the skiddies that they’ve left, if there’s no toilet brush.
Anyway, it isn’t just confident, outgoing 30yo women who have periods, but also painfully shy 9/10yo girls – and anybody in between of whatever age.