Air conditioning vented indoors?
A "ductless" a/c system would appear to be the solution for this condo. You must exhaust the heat and humidity to the outside. Google "ductless mini split a/c". 

Having a window a/c unit exhaust to the sun room would be completely unacceptable. A window unit used in this way would be by far the cheapest way to cool the bedroom, but would destroy the utility and aesthetics of the sun room. It would almost certainly be rejected by the condo association.

The condensing unit of the ductless system would be on the ground outside or hung on the outside wall and the air handler/evaporator on the wall in the bedroom. Refrigerant and electrical lines would connect the two units. The tubing to carry away the condensed water could presumably follow the same path and drip onto the ground outside.