As johnwasser says, you don't need the bootloader to use the watchdog timer. HOWEVER, there is a problem you may have run into that the bootloader "solves". The problem is that when the watchdog timer expires and causes a reset, the watchdog is still enabled. The processor needs to complete the data initialization that occurs before setup() is called, before the timer expires again. Otherwise the watchdog will cause another reset, and this will repeat so that your sketch never gets the chance to reset the timer. The bootloader "solves" this by disabling the watchdog.
So it comes down to what you have in your sketch whose static initialization takes longer than the watchdog interval. The usual culprit is the LiquidCrystal library, which has a totally unnecessary "begin" call in its constructor, taking 60ms to execute (longer than the longest available watchdog interval). If you are using the LiquidCrystal library in your sketch, you need to remove this call from the LiquidCrystal library source code, otherwise you can't use the watchdog timer.