I'm sensing from your post you are looking for a way to regulate temperature in your bedroom on demand. There is no easy or cheap way of doing this. Any portable A/C I know of requires venting to outside air. My suggestion would be a fan. Either ceiling mounted or portable. Gives the option of increasing or decreasing air flow, thus cooling more or less, on
demand. Make sure all system air returns are unobstructed.

1.An alturnative is to cool the room by increasing existing A/C
supply air flow, to that room. (You will not have on demand control).
If your a/c system was never 'balanced' have a professional do it, emphasizing your desire to increase the bedroom flow as much as possible without sacrificing the rest of the house cooling. Your option!

2.Try looking at the supply duct, at the trunk line. If there is a damper in the duct run, open it to full open (if it is not, already). The damper handle should be parrallel with the duct,(Length wise). While you are in the area of the duct run check it for tears (flexible tube),obstructions to air flow, crushed sections or valleys. Make sure the duct is fully connected to all system parts and air tight. Make sure any taped joint is secure. This applies to metal duct as well.

3.Make sure the bedroom supply register, damper, is fully open.
(If the room is isolated from the return air duct a closed
door can effect the CFM flow for that room).

4.Afer any adjustments to the system, check the rest of the house to estimate adequate air distribution/balance.

5.There are thermostatically controlled air dampers available. Recommend professional consulting and installation.

6.Try the advice of the other responders if my suggestions fail... Good luck, stay cool.