SQL Server Transaction insert object list?

I would like to be guided, I have a stored procedure in a transaction that does the following:

The Sales table has a trigger that triggers when the "ProductId" column is changed, this to record the changes made in the "Sales" table in a blog

My problem: It generates a timeOut by default it was 30 sec, I have changed it to 2000 sec which is approximately 33.3 min. but time runs out and sends the timeout exception, can I optimize my procedure to not have that problem? I understand that once the transaction starts the tables are blocked, I need tips to complete the transaction.

    UPDATE dbo.Cliente
    SET ProductoID= @ProductoNuevoID,
    WHERE ClienteID= @ClienteID;

    INSERT INTO dbo.ClienteProductoBitacora
    (
        ClienteID,
        ProductoAnterioID,
        ProductoCambioID,
        FechaCreacion,
        UsuarioCreacion,
        UsuarioDominioCreacion
    )
    VALUES
    (   
        @ClienteID,
        @ProductoAnterioID,
        @ProductoCambioID,
        GETDATE(), -- FechaCreacion - datetime
        User_Name(),        -- UsuarioCreacion - varchar(50)
        @Usuario         -- UsuarioDominioCreacion - varchar(50)
    )


    UPDATE dbo.Ventas
    SET ProductoID= @ProductoCambioID
    WHERE ClienteID = @ClienteID;

    END
    GO