Just been in the same situation with a car! As Toureman says, you will need to go to your local DVLA office.
Do you have the green "New Keeper " section of the V5C? (Vehicle Registration Document/"log book"), the seller should have given it to you before they sent the rest of the form to the DVLA. If you do, then you can get a new V5C in your name for free (it's posted out to you, you don't get it there and then) and tax the bike whilst you are there (need to take MOT and Insurance documents) They will ask you to fill in forms V10 and V62.
If you
don't have the New Keeper section of the V5C then they will charge you
�25 to issue you with a new V5C!! (You will have to fill in forms V10 and V62 as well). You can't tax the bike without either the New Keeper section of the old V5C, or a new V5C in your name.
List of DVLA local offices is on this page;
http://www.direct.gov.uk/en/Dl1/Directories/Us efulContactsByCategory/MotoringContacts/DG_100 12974