How can I get rid of these bugs. It has taken over new blooms, sprouts etc.
I suspect they are mites, or the larvae of some moth.
Is your Jasmine in a pot? If so, set the plant aside from other pots asap. If not, that is okay. Go ahead and examine the plants around your jasmine in either case to see if they have also been attacked. If it is limited just to your jasmine for now, you are lucky so far.
First, remove any dead branches, dead or dying flowers and set them in a bag. Do not use the bag for compost. Move it to your garbage disposal asap.
Using a hose fitted with a sprayer, or using a watering can, hit the plant generously with a solution of diluted soap in water. Do this profusely to get rid of the bugs. Do this a couple of times and really work it in there. Then, follow it up with water. Check your plant visually and make sure you don't see the visual presence of any of these white guys. Repeat this check over the next few weeks on a regular basis.
If you don't start seeing immediate improvements, you might have to consider insecticides.
If you mean the little, narrow white specks visible on the leaves and flower stems in your picture, and they're clustering on new growth and flowers, it's an aphid infestation, possibly whitefly. You haven't said where you are in the world so its difficult to recommend a treatment, but any insecticide which treats for aphids (whitefly, blackfly, greenfly) should work; neem will also work on most aphids and is less harmful in the environment than some of the more heavy duty systemic insecticide formulations.
If there are other symptoms on the plant you haven't mentioned, and which aren't visible in the photo, please edit your question to add more information. Cestrum nocturnum is prone to attack by leafhoppers in some parts of the world, but you'd be seeing leaves and shoots being eaten were it those.