You should have a professional cleaning to remove the cement from the teeth and below the gum line, it's always recommended after the removal of ortho. The "white stuff" is either plaque or demineralized areas cause by the acid in plaque that is left on teeth too long etching or initiating the decay of these teeth. Plaque can be brushed away, if it’s not brushing off then its demineralized areas. Take care of getting your teeth cleaned and have these "white" areas evaluated first. You can discuss bleaching with the dentist then. He can explain the different methods available. Hope I've been of some help and good luck.

additional information: You've already had impressions made for your retainers, these same models can be used for bleaching trays to be made from. There is no need to go through the impression process again, nothing has changed (crown work) since these were made. Just ask your orthodontist for them if he didn't give them to your already.

And thank you Dr. Albert, that is so true, a high speed hand piece isn't always needed to remove the orthodontic cement.