At the very least, I'd let him settle in for at least two days before trying to bond with him. Really, it depends on the bird. Noah had been through a lot right before he came to me, but he was calm, confident, and really wanted attention. So, the first day he came to live with us, I spent hours sitting by his cage. I read to him, talked to him, showed him different foods, gave him different foods to try, etc. However, this was a unique case. For most birds, this attention would have been extremely stressful.
Anyways, when it comes to bonding with budgies, I recommend interacting as little as possible for the first few days. After this period, I recommend sitting 6 feet away from his cage, at least three times a day, and reading to him. Even better, sit perpendicular to his cage. Budgies are extremely skittish, and they don't like sudden movements, sudden sounds, or people looking at them. If you want to glance at him once in a while, fine, but you should keep one eye closed, and don't look at him for more than a couple of seconds. Humans have forward facing eyes, indicating to other animals that we're predatory, which freaks birds out.
Right, so back to the reading thing. The first few days you read to him, treat it more like you're reading aloud to yourself. Don't try to engage him in the reading. After a few days, start looking at him every once in a while while reading aloud, and pause once in a while to discuss the book with him, ask him how he's doing, etc. After a week of this, he should start to become a lot more comfortable around you.
Oh, I also recommend moving your chair a few inches closer to his cage every few days. However, if he becomes uncomfortable with how close you are to him, move your chair away from his cage again. He's the one who decides how quickly your relationship progresses—not you.
Also, I recommend covering at least half of his cage with a towel or whatever. This will make him feel safer. Some other things you can do to help him adjust is to give him a swing, spray millet, and a couple of mahogany pods. All new birds are given these things while in quarantine to help them adjust. Mahogany pods are these soft pods that budgies absolutely love shredding.
Once he settles in more, I recommend playing songs for him to figure out what sort of music he likes. I recommend trying the following songs:
500 Miles
Alejandro (Lady Gaga)
Cotton Eye Joe (The Rednex)
Everytime We Touch (Cascada)
Gangnam Style (Psy)
Tubthumping
Let's Get it Started (Black-Eyed Peas)
Paso (Sak Noel)
Put Your Hands Up for Detroit
Seven Nation Army (The White Stripes)
Stuttering (Fefe Dobson)
Völlig Losgelöst
Bósi is guaranteed to like at least one of these songs. If not, he may be deaf (or really introverted).
Right, after he's comfortable with you around his cage, hold spray millet for him to eat (keep your hand outside the cage). After he's eaten the millet while you've held it for a few days, grasp the spray millet further up so your hand is in his cage, requiring him to move closer to your hand.
Anyways, once he's confident while taking food from your hand, clicker train him, then target train him.
As for diet, I feed my guys 1/3 pellets (Goldn'obles III and Totally Organic Pellets), mash, at least four different fresh organic veggies, and organic millet. My birds have developed food sensitivities, so it's a pain to feed them. I'd recommend making my birdie bread recipe titled, "The Most Nutritious Birdie Bread". I'd also recommend feeding him the parakeet seed mix from Dr. Harvey's (buy online), and Petite Hookbill Legume Blend by Goldenfeast. Also, I recommend providing him with a dish of dried lavender. Buy this in the herb section at the health food store. And please make sure it's intended for ingestion. If you get lavender elsewhere, it will probably be soaked in toxic chemicals.
Look up "Avian Organics mash" to get an idea of what mash is. Also, only give him human grade products. None of that nasty animal grade stuff. Also, buy him a Manu mineral block. And, once his cere turns blue, put in a tiny dish of bird grit. Make sure it's the kind with soluble AND insoluble grit. Budgies instinctively seek out grit, and he could end up getting himself into trouble if he doesn't have access to appropriate grit. Just wait till his cere starts to turn blue, as young birds can sometimes make themselves sick from eating inedible things. If he's still learning what is and isn't food, he could end up eating way too much grit, mistaking it for food.
During the average week this summer, my birds may end up eating: wheat, oats, barley, buckwheat, quinoa, wild rice, brown rice, flax, chia, sunflower seeds, pecans, macadamia nuts, pine nuts, lavender, chamomile, dandelion, freshly collected grass seed, chickweed, purslane, broccoli, spinach, Swiss chard, parsley, Romaine lettuce, clover, mung beans, lentils, chickpeas, peas, millet, carrot (leaves and/or root), aphids (not often since they're a pain to harvest), tomato, nasturtium blossoms, celery, kelp, and dill. Normally, I'd also give them peashoots, beet greens, and other things, but I didn't have enough room to plant everything I wanted to this year. Next year I want to grow Peruvian plants for Noah. I'm also going to collect pine cones for the kākāriki so they can eat the pine nuts out of them.
Oh! He's been handled since he was little? You should have no problem bonding with him, then!
I do this couple of times a day. I've given him spinach and lettuce. One time tiny bit of apple slice and egg. He really loves it! He seems very calm and I will take is with patience. Again thanks for the tips! He loves music! 
I will update in couple of days-week
