Maybe you or someone you know has already slipped and fallen in the bathtub or shower. I won't bore you with statistics, and you didn't come here to read them anyway. You have a hazardous bathing area in your home and you want to fix it quickly and, hopefully, inexpensively.
I looked on the web after my slip-and-fall and saw "bathtub safety kits" of various types, starting at about $100. But I did some experimenting and found something that is effective and a whole lot cheaper.
You will need: white vinegar, plastic wrap, paper towels.
Here's what you do: Moisten a finger and run it across the tub surface, noticing traction (or the lack thereof). Close the drain on your bathtub or shower. Cover the slippery area with paper towels, double thickness. Pour the vinegar onto the paper towels until they are all well-soaked. Cover the wet paper towels with plastic wrap. Wait 5-8 hours, then remove plastic and paper towels and discard. Rinse the tub with water and wipe dry. Repeat the moist-finger test and observe difference.
Repeat as necessary. For my tub, one treatment worked great. That was several months ago and it still provides excellent traction.
Why it works: Porcelain is porous. Over time, skin oil, soap residue, cleanser residue, shampoo and everything else packs into those tiny pores. Cleanser will not remove it. Steel wool or a wire brush probably would, but it would ruin the surface forever. Vinegar is about 5% acid and will actually dissolve the residue without harming the porcelain.
This may not work for every tub surface, but if it works for yours, you will be avoiding a common hazard in many homes .... without a huge expense.