The procedure suggested by steve will give you the fastest possible pop (possibly around a tenth of a second?). R = 4.5V / Isc.
I don't know what temperature it takes to pop a balloon, but here are some practical values of approximately what to expect from an 1/8W (0,125W) resistor in free air.:
150 ohms = 60mA = 0.5W = 90 degrees C.
82 ohms = 110mA = 1W = 150 degrees C.
56 ohms = 150mA = 1.4W = 200 degrees C.
I'd suggest to try using an easily manageable 47 ohm 1/8W resistor, which will yield a considerable temperature but which still won't go up in smoke.