Bleeding is done from the engine side of the bulkhead - there's a bleed screw there that you can open with a coin or summat.
I have to say, opening that screw always gets the air out of my (diesel motor) matrix.
If you have rubber mats, lift the passenger one and see if there is any water under it. The heater matrixes corrode and leak making the passenger footwell damp. Mine is ringing wet under the mat. Been like it for a while, need to sort it!