Jeez, that's a challenge... I have to admit that bathrooms are not my preferred identification setting... in fact any spider (or indeed anything with more than 4 legs) that comes anywhere near me while I am in such a vulnerable state (as one often is in that room) gets summarily squished!! I'm from the West Coast and it wasn't unusual to find SLUGS in the bathroom there, which means I learned to always always always turn onthe light...
I don't know how much I can help with ants, there are about a gazillion different kinds, but yours may be some kind of wood ant. If they are bothering you put down some borax powder and/or peppermint oil - they don't like it very much.
I've caught the odd bug in my teeth while cycling, never thought of mounting a net!