I have exactly the same problem as Drop-D. If I haven’t accessed my WD Passport Essential SE in the last few seconds, my next access is delayed a couple seconds. This is true on either write or read access.
I’ve been in touch with WD tech support on this issue. They suggested I make sure my drive has the latest firmware. To this end, I selected my drive and OS from http://www.wdc.com/wdproducts/wdsmartwareupdate/ and downloaded the firmware installer. It upgraded my firmware from 2.011 to 2.019. This didn’t solve the problem, but it seemed to reduce the delay to about 1.7 seconds.