Busy Lizzies are correctly called and often sold as Impatiens. To combat disease they have been crossed with ‘hawkeri’ a variety from New Guinea.
The bigger the plants you buy the less impatient you need to be but beware of frost, a sure killer.
I have just received 72 plug plants that were little more than germinated seeds but I have followed the instructions repeated below:

Pot up plug plants and grow them on in bright, frost free conditions.
While the plants are still small but with more than 2 sets of leaves, pinch the growing tips out to produce a well branched, compact plant.
When all risk of frost has passed I will acclimatise the Busy Lizzie plants to outdoor conditions over 7 to 10 days, prior to planting in their final positions.

Growing Habit
This robust New Guinea Impatiens is strong growing and mildew resistant so you can rely on a fantastic display from Busy Lizzie ‘Divine’.
Its large flowers in a mix of red, orange, lavender, white and magenta are perfect for adding colour to patio pots and garden borders
Plants should withstanding wet, dry, cold or hot conditions throughout the summer. I can’t help but think they will like a regular drink and some humidity so I plan on a couple of plants in pots in the house and greenhouse.
Height: 30cm (12″). Spread: 35cm (14″)
Busy Lizzie ‘Divine’ flowers endlessly in a bright mix of colours from June to November.