My dad has got an urban bitter gourd garden on landed property. He grows the melons out of polystyrene boxes.
Recently one of the neighbors gave him white bitter melon seeds to grow. After few weeks he manage to grow out 2 white melons.
One thing about this plant is that it really likes a lot of sunlight. While the taste is bitter, it do gets attacked by insects, so my dad has to wrap up the melons once it starts fruiting.
I see these melons being sold in JayaGrocer also.