If you want to keep the weeds down, I would recommend putting some weed suppressant fabric down before putting the bark down. It really helps to keep weeds at bay.

You don't have to put anything underneath the bark if you don't want to, a depth of 2 inches of bark suppresses weeds anyway, but weed membrane fabric from the garden centre if you do, as Lizfisher suggests.

I don't put anything down under the bark.