I would use 2 ubiquity loco m2 point to point aps. They are about $50 each, you will need 2. I use them for events to get internet to remote locations. We even use them to stream sporting events.
One of these:
http://www.amazon.com/Ubiquiti-NanoStation-locoM2-2-4GHz-Outdoor/dp/B004EGI3CI
You'll have it connect to the WiFi hotspot, but you'll probably have to login every once in a while.
People have gotten off the shelf wrt54g's to go hundreds of miles with antennas and clear line of sight. All you need is a high gain antenna at either end, although your biggest improvement will come from getting the link to not have to traverse all those walls. It would most likely be cheaper (and more reliable) to get a pair of dedicated endpoints with integrated antennas than to get antennas big enough to shoot through all of that, plus you wouldn't have to worry about FCC rules since you'd be doing point to point instead of point to multi-point. You can run higher power PTP.
I would think a pair of ubiquiti nanostations mounted outside would do it, but without being on site I can't give any better advice than that.
http://www.amazon.com/Ubiquiti-Nanostation-LOCO-Outdoor-802-11g/dp/B004EGI3CI
Run an ethernet cable to that unit and mount it outside. Inside, connect a wireless router to the other end of the ethernet cable. It comes with a power injector that goes inline with the ethernet cable to supply power.
Needs to be set it in station mode, pretty easy to get going though.
You might also look at a set of the M5's or calling the microwave company to setup a link to you.
That is a pretty brutal layout. Bathrooms are typically hell on RF due to construction materials like tile, glass and other hard/dense/flat surfaces.
I find it interesting that you are getting better RSSI from 5GHz than 2.4GHz... I don't know anything about the tx power of the Asus radios (and I'm too lazy to look it up), but given the distance and attenuation, 2.4GHz RSSI should be much better than 5GHz in your room if both frequencies are transmitted at the same power level.
The problem with directional antennas is that they may help improve the signal to the client station, but unless the client station has a similar antenna, there is a chance the transmissions from the client may not even begin to match the data rates on the downstream.
Also note that you should get 3 of those directional antennas for that router (MIMO - there are actually 3 transmitters/antennas). Ideal alignment would be in 3 different directions, all somewhat facing the bedroom. something like " \ | / " (lines representing the transmission direction of each antenna).
An alternative would be to try a pair of 2.4GHz Ubiquiti Nanostations and bridge the remote end to ethernet.