Kinda like your way... but the compiler doesn't like where I've placed astericks:
USE [TrackIT]
GO
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
CREATE TRIGGER [dbo].[trUpdateBulkPurchases]
ON [dbo].[tblTransactions]
AFTER UPDATE
AS
BEGIN
UPDATE tblBulkPurchases
*(tblBulkPurchases.PO_Number,
tblBulkPurchases.Quantity,
tblBulkPurchases.Transaction_Number,
tblBulkPurchases.Quantity_Remaining,
tblBulkPurchases.Unit_Price,
tblBulkPurchases.Software_Description,
tblBulkPurchases.PO_Date,
tblBulkPurchases.PurchaseCostCenter,
tblBulkPurchases.HeatTicketNumber,
tblBulkPurchases.PurchaseAccount,
tblBulkPurchases.Transaction_Date,
tblBulkPurchases.Transaction_Type,
tblBulkPurchases.SoftwareShortName)
SELECT
i.PO_Number,
i.Quantity,
i.Transaction_Number,
i.Quantity,
i.Unit_Price,
i.Software_Description,
i.PO_Date,
i.PurchaseCostCenter,
i.HeatTicketNumber,
i.PurchaseAccount,
i.Transaction_Date,
i.Transaction_Type,
i.SoftwareShortName
FROM INSERTED i
inner join tblBulkPurchases
on tblBulkPurchases.Transaction_Number = i.Transaction_Number
WHERE Transaction_Type = 'Bulk Purchase' *
GO