Good ! I understand what you said about the power increase. By the way it show that the port A is an output.
It seems that you are not taling about the same chip.
The one I use have
reversed OE pin. ( /OE )

I have all /OE and DIR to GND, so it good for B to A for the two bus I think.
But I still cant understand why the serial link 1A2 1B2 works like a charm, and on the other hand, the simple power on on 2A2 2B2 only works when the SIM900 is already on and is going to shutdown.
Maybe it is just about the 2.8VVD_EXT from the SIM900 module that is not realy good when the SIM900 is off. But I still see 2.9 V on it.