the only showers i've ever used are the solar powered ones in the greenpeace field. they used to run a system where you took a ticket and came back at your alloted time, but they weren't running when i went last year (not sure if it was just because the queues weren't that big - it was raining). the last couple of years they've reduced the queues by making the showers completely open - they are single sex, but once you're in the boys/girls area it's just a bench along one side for changing, and a row of showers along the opposite wall with greenpeace peeps chivvying everyone along to keep the queue moving.
some girls went in in their bikinis or pants, whatever you're comfortable with.
i think there are also showers near the kids field/family camping, but i've never used them - always hear that the queues are massive? not sure about down near john peel.
there's also showers at the saunas and stuff, but they tend to keep them for sauna customers only if it gets too busy.
you're not allowed to take any products into the showers, the festival provide an all-in-one biodegradable (?) hair and body wash for you to use, so you might like to take a little container of leave in conditioner with you if you've got long tresses.
and if you are washing your hair under one of the taps don't forget that the run-off just drains straight into the ground, so take products that won't kill the fish