I think children have the easiest time developing social skills if they are with true peers - others who share common interests, who communicate with them easily, and who have similar levels of mental, physical, and emotional development. Obviously, gifted asynchrony makes it hard for gifted kids to find this anywhere outside a self-contained gifted classroom, and for HG and PG youngsters, it might not even happen there. The greater the obvious differences (both in number and in magnitude) between the gifted child and the other children in the class, the harder it will be for the gifted child to feel like they fit in and to develop good social skills and appropriate peer relationships at school.
For kids whose vocabulary, interests, and intellectual development are so far ahead of the norm that they find it frustrating to even try to communicate with their age peers in pre-school and Kindergarten, grade skipping is often a godsend, because the physical differences between the older children and the younger gifted child are typically not as significant in these situations as the mental differences between the highly gifted child and age peers.
I don't think that going to school with peers who don't understand you or share the same interests does a lot to improve shyness or develop good social skills, so I'd be sure to provide lots of opportunities for a shy, not-very-socially adept kid to interact with others who were at a similar mental level and who had similar interests, so that there was some actual payoff for the child for putting forth the effort of trying to interact.