Mould low down on an interior wall suggests that the dampness that's causing the mould may be comming from outside - if it was an internal condensation issue the tendency would be to have condensation forming higher up in the room.
Check the outside of the bay - rotten wood or cracked masonry may be letting in water. The path may be raised higher than any damp course in the brick line - a gutter may be leaking.
If all these are good then the dampness might be internal condensation and airing the room as you do is a good thing - try to keep the heat down in the room when you're not using it - continue to leave the windows slightly open whenever possible - keep the door closed to stop warm air from the rest of the house especially from kitchen or bathroom getting in there. Scrub off the mould with dilute bleach and dry it well and possibly scrub it again. Consider a dehumidifier.
Keep drying the wetness to stop the mould forming again and as soon as the weather allows throw all the windows open and turn all the heat off for as long as you can - all day Saturday & Sunday perhaps. If you have suspended floors (wood rather than concrete) lift the carpet and prise up a piece of floorboard near the bay window - look through with a mirror and a torch to see if there's any dampness in the underfloor void - if so check the airbricks - poke a stick through from outside.
Put an old dry towel on the inside windowsill just to check that it's not run-off from condensation on the windows.
The mould will be from dampness - the dampness will be from inside (condensation) , outside (rain getting in) or below (high water table).
Avoid specialist firms offering damp proofing - they will always find a problem and their process will always be the only solution for your problem and it will always cost a fortune and it will seldom be a permanent fix. If you do hire anybody a good independent builder is your best bet.
Good luck...
Peccavi
February 2009