1) If it has no earth connection then either it doesn't need one, or it is a nasty dangerous item that should not be used.
a)On the assumption that it's a reputable make, and carries stickers indicating that it meets BS/EN standards, or is CE marked or has BEAB approval etc, see if it has the symbol for a double-insulated appliance (a square within a square), or see what the instructions say about earthing. If it is double insulated, it does not need an earth, and attaching one might make it less safe.
b)If you bought it cheap in the market, or it was left to you by your dear old gran, or you found it in a skip, and it has no comforting safety labels, don't use it.
2)Taking a connection back to the CU as you describe would not be supplementary bonding, it would be earthing. Supplementary bonding would be connecting the earth conductor of the appliance to the bonding in your bathroom, not the CU earth.