A much higher exchange rate.
A much larger group of people buying and selling bitcoins.
A wider distribution of bitcoins.
When these three things happen, one person (with either a ton of fiat money or a ton of bitcoins) won't be able to move the market several percent with one purchase or sell.
These things take time. As long as the network doesn't fail, they will eventually happen.
Until then, don't expect a stable bitcoin.
AMEN !