You need to go to Al Rawnaq in the souk area. Turn off the Corniche and go up Grand Hamad Street. Turn left at the disused traffic lights by Souk Al Ahmad. Go along to the end of this street, turn left and just around the corner on your right is the small shop front of Al Rawnaq. Inside, the shop is huge and they have an extensive assortment of beads upstairs. They also stock the world's widest range of hair accessories plus ribbons, artificial flowers and lots of cheap jewellery.
Make sure you go to the correct branch. Nearby, Al Rawnaq also have a shop selling shoes and handbags.