Bathroom-generated Recyclables Overlooked

I realized recently inside my private residence that my own level of participation in natural-resource recycling varies dramatically depending on the room of my residence where a trash item is generated.
In my bathroom, unfortunately, I have yet to install a recyclables bin separate from my trash can in that room of my residence.
My only recyclables bin that I'm currently using is a 13-gallon recycles bin that I have placed inside a closet in my kitchen. I strive to empty that bin twice per week by placing recyclables at public outdoor recyclables bins that are situated nearby.
I plan to purchase a small recyclables-collection bin in my bathroom, and then toss into that bin for future recycling such items as:
----an empty plastic container of alcohol-free mouthwash;
----an empty plastic bottle of contact lens solution;
----an empty plastic bottle of bath oil;
----the plastic lid to my can of shaving cream;
----the plastic cap to a tub of toothpaste;
----the plastic cap to the disposable razors I purchase;
----possibly the plastic disposable razors I purchase (though they are an item with some metal that possibly could be recyled separately);
-----possibly the plastic deoderent dispenser I purchase.
One reason why many of the bathroom items tend to get overlooked as recyclable items is that the manufacturers of those bathroom products often fail to clearly state on the packaging for those products that "this is a recycable PLASTIC ITEM, PLEASE RECYCLE!," OR WORDS TO THAT EFFECT.