2 ways I've had success with are:-
1) from the outside, remove the joint from the pipe leaving the house and send a bottle brush on a suitable extension into the pipe and clean!
2) take a cable from an old bike, pref with a frayed end, and carefully insert down the drain in the showerbase. Then twist whilst slowly withdrawing! (should add insert the frayed end first)
handyman Malc, January 2012