The front most bulb, there is a tiny green nub near the leca. I am asking what should I do to make that part grows, i.e. should I start fertilizing? Or should I just water it till the nub full develops to some sort of a root before fertilizing?
This is not a cattleya, but it is a close cousin; it is an encyclia.
It's hard to make out the nubbin. However, your care of the parent plant is obviously working, so I would continue on the same way. The new growth should not need anything different. I would avoid pouring water over the new growth as it develops, to keep any drops from being trapped inside the new growth. Once the growth is fully open, the chance of rot is much less.