I too have had these little things - before I took down my shower doors, I would find them coming out from under the grimy tracks. I'm not sure, but I think they became flies. (does that make any sense?) I noticed some little flys that looked slightly bigger than fruit flies around this same time. Anyway, when I got rid of my doors and frame,(and the wet grimy areas) The bugs and flies disappeared.
It sounds like a LEECH, which is used in laboratories to draw blood from skin in operations, and in certain swamps they are plentiful. A silverfish is silver, not black and is tiny, fish-bodied, not flat. Don't think it could be a silver fish. Can't imagive how it got into your tub unless you have a plumbing leak or someone has played a cruel joke on you? God bless your search for the truth. : )
Angie - it sounds like they might be Silverfish. They like damp places like bathtubs and under sinks. If you go to Google and type in "Silverfish" you will get lots of information; also pictures so you can tell if this is your problem. Hope this helps.
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