Is giving away items as bribes to other players restricted to table cards?
It clearly says that you can't trade non-items or items in your hands, and there's nothing contradicting that.

Being able to reveal your hand does not imply you can trade cards in your hand. You might show your hand to reveal that you are able to affect a combat as a threat or to show you can meet a promise.

Being able to trade carried items does not mean you can trade items in your hand. Carried items are not in your hand. Quite the opposite, the items you carry are on the table. ("[Cards in play] are the cards on the table in front of you, showing your Race and Class (if any) and the Items you are carrying.") Not all of the items are you are carrying are in use because some are single use items, some aren't usable by your race or class, some items would occupy an item slot that's already occupied, etc.