Another vote on the zip strip.
What works even better, if you have one readily available, is one of these.
While the tool is something most auto mechanics have, I find it works quite nicely for removing those "dead-cat" mats of hair that build up in sink and shower drains as well.
You can get a firm grip on the clog, even better than with a zip strip.
Note that for a shower, sometimes it is easier to pull out the drain lever mechanism, and go down into the pipe via that opening.--
Shine on you crazy diamond...