Sorry, wasn't reading well. The problem is that you have a malformed UPDATE statement.

CREATE TRIGGER [dbo].[trUpdateBulkPurchases]

ON [dbo].[tblTransactions]

AFTER UPDATE

AS

BEGIN

UPDATE tblBulkPurchases

set PO_Number = i.PO_Number

, Quantity = i.quantity

...

FROM INSERTED i

inner join tblBulkPurchases

on tblBulkPurchases.Transaction_Number = i.Transaction_Number

WHERE Transaction_Type = 'Bulk Purchase'

GO