A plastic cup with a faded lion on the front. That is what was kept in our shower when I was pretty young at the first house I remember living in to rinse any hair that was sticking to the tub when finished bathing. I think it was from The Ground Round, remember them? I didn't shave back then, so I didn't get much use out of it.
Any plastic cup will do. After shaving, use clean water to wash away hair that's still clinging to the tub. If you don't, it dries and sticks and has to be scrubbed off. And whoever cleans the bathroom will get upset when it could have been easily prevented. Take my word from personal experience.
Longer hairs that shed from the head usually make their way to the drain with some of the shaved hair. So don't forget to use a filter on the drain and clean that out after every shower! Otherwise it backs up and doesn't allow the water containing floating hair get filtered and go down the drain. A ring of hair around the tub is not a pretty picture for the next person who pulls back the shower curtain.