As someone who was bullied at school, let me assure you, the only socialisation I received from the experience, was an appreciation for how fucking horrible humans can be.
There are other ways to socialize kids besides school. As I understand it, things like field trips and social gatherings are an important part of a well balanced homeschool experience.
Instead of just studying about government from books, take a field trip to City Hall, observe a public meeting and talk to people there.
Spend time with other home school families (via homeschool associations) and other families in general. Take trips with them. Let the kids hangout among themselves.
Homeschooling gives you that freedom.
Anecdotally, I personally know homeschooled young adults that are confident, have great social and communication skills and are doing very well in life thus far.
I feel that motivation of most homeschoolers - a lot of time fuelled by their own bad memories - is to provide an "adequate", contained, controlled chicken coop. Life is anything but that. I can't believe one can go in with a pharmacy scale and make a just fine sampling of daily societal life.
Source, somehwat: I was also bullied in school a lot, but in the end I think I could learn and grew from the experience.