Im a high school student, and I have been a very sick child all my life and have been bullied on very often.
I can say that if my mother had home schooled me, I would NEVER have gotten the social skills I needed. Im still a shy person, and dont have the greatest social skills, but they are at a decent level. I believe good social interactions can be had in homeschool, however.
On the other hand, i have always been a very sick girl. I constantly got the stomach virus, ear infections, the flu, you name it I got it. And now that I have been diagnosed with IBD, it has only been worse. Really, the only way to help this is to teach him tips on how to avoid getting sick - wash your hands, dont have close physical contact, avoid people who are sick, ect.
As for bullying, it hurt me as a child, and it caused many problems, namly my social awkwardness, I think. But it also made me a MUCH better person in the long run, because I perservered. I now know how to be a better person, because of their foolishness and ignorance. However, some people can handle bullying and some can't. Its just a matter of personal difference. Just, WHATEVER you do, stay on to the teachers and the principal about this bullying problem!!! Dont let it slide under the radar, because if you let that happen, it will just continue.
This is just my 2 cents worth. I honestly think the success of homescholing depends on the parent. If you do, make sure the child is given social interactions often with his own age group, and plenty of time outdoors and can participate in things like the arts and sports for enrichment. Expose him to the real world. All in all, it could be both bad and good.
Like I say, nothin is perfect. There will ALWAYS be problems with something.
good luck, I hope you find a solution to the problem.