I've had mixed results with my budgies. Felix is fearful, but, considering he was found in somebody's backyard completely skin and bones with an overgrown beak that needed trimming...I don't really blame him. He runs from me. But, when caught, he'll sit peaceably on my finger or my shoulder until someone tries to touch him. This is after several months of having him out everyday.
Snow doesn't really like people. She bites when you're trying to take her out of the cage, and she runs off while you're holding her if you give her a chance. She's gotten better in recent days, but she's still not content to just BE with me. She'll perch on a finger, or on a shoulder if you make her, but any opportunity more entertaining than perching there is likely to attract her attention and make her leave.
Pippin, however, is a dream, as far as the budgies go. He's to the point where he goes and runs errands with me, and used to go to work with me. When I'm not entertaining him enough, he'll leave my shoulder and wander around a little bit, but usually only when we're at home. When he's off with me, he sits quietly and peacefully, and will let other people touch him and hold him (until they wander away with him too far from me...then he jumps off their shoulder and comes running to me...he does have a few mommy issues). He steps up absolutely beautifully, and he's started mimicking the tones and rhythms of human speech without the actual formation of words. He's been an easy case most of the way along. He and Snow were my first birds, and therefore had my pretty much undivided attention more than not. There were many long sessions of sitting in my bathroom on the floor with both of the birds getting them used to me, and fetching them after they'd jumped off my finger.
I think all of them would benefit from being an "only budgie," as far as taming them. But I'm glad I got the original pair, and then Felix as a rescue situation two weeks later, for their own health and peace of mind. I know they're personally happier in my life situation as a trio, and, as much as I do sometimes wish they'd be more interested in ME and less interested in each other...it's a sacrifice I made for them. Even in their trio, though, they're a wonderful set of birds, and I adore them completely---even Snow, who CAN and DOES bite hard enough to draw blood.