Take a cotton ball and wet it generously with rubbing alcohol so it's soaked. Then sprinkle enough salt on it to cover the ball. Then scrub on the inside of the bowl.

The alcohol/salt mix will drip downward and start eating through the gunk in the stem. Take a Q-tip and pour some alc. on that. Push it into the stem first downwards from the bowl, then upwards. Push it through enough times and be sure the cotton is scrubbing the glass well. You may need to repeat this if the buildup is bad.

The key to removing heavy gunk is the salt.