Bailout should weaken currency. Let's see how it has unfolded since September 2008. Some currencies have fallen significantly against others. Due to this US $ and Japanese Yen have gained their strengths. Yen still remains stronger against US $.
Since September 2008, governments around the globe have bailed out many industries. Where do governments receive the money to bail out. Well, they borrow. They borrow from one another and public. This borrowing takes places against IOU or bond issued by government. By doing so governments increase national debt. When supply of bonds increase suddenly, yield should have been higher to attract buyers. But, due to the plunging equity and corporate debt markets, investors are purchasing government bonds as a safe heaven investment (US Treasury bonds are free from default risk, but still exposed to market risk). This has driven the yield close to 0%. Once national debt increases, currency would lose strength.
Investments move from low interest rate to high interest rate countries for higher returns provided the exchange rate risk is within the investors tolerance. Exchange rate has anything but normal. Many European, South American and Asian currencies have been in a roller coaster ride for over the past 6 months.
US $ has gained strength against GBP, Euro, Ruble, Indian Rupee and all the commodity currencies (Canadian $, Australian $).
Yen has gained strength against almost all the major currencies. Why is the anomaly? Well, this because of national savings.