> The problem I have is when I am sitting on my laptop next to AP-A (before i connect
> to the Wireless Network, that has the same SSID) the signal strength is full bars.
> So I connect. Right after I connect I have one to two bars of signal.
I have observed that behavior using the 'Connect' button in View Available Wireless Networks on XP. But it wasn't from connecting to the far AP. I think either WZC can't really tell them apart or the number of bars just isn't accurate until after it makes the connection. Turn off AP-B to ensure you're connecting to AP-A and you should still see the same thing happen (number of bars drops off full after connecting).
Does your laptop's wireless driver have tunable roaming decisions?
e.g. see attached.