This may be only anecdotal evidence, but I would consider being bullied for a bit a positive net influence in my life for a couple reasons:

• I have always been somewhat arrogant. While being bullied did not decrease said arrogance, or even immediately result in any changes, when I looked back and saw how people treating me made me feel, it became somewhat of a motivator to mask some of my arrogance to spare others feelings. As knowing the right people can make a large difference in various opportunities, I feel some opportunities I have received had I not learned to mask said arrogance.

• Eventually you learn to deal with it. While bullying to the extreme someone kills themself is clearly bad, and in other cases it can seriously damage people's psyches, for others "what doesn't kill you makes you stronger". I learned that while there are some people you can "make" like you by acting differently, some people are just shitty people and not worth your time. There's a balance between the social benefits of people liking you and the stress of ping too far to being a people pleaser.

This is far from an advocation of bullying, but without it those lessons would have been much harder to come by.

I feel the social benefits, even accepting the risk that bullying could happen and have a significantly negative influence, outweigh a lot of the benefits of homeschooling. I would most likely take an approach similar to my own parents'. I went to a public school, and when I came home I had a library of thousands of books to browse and read from. I still was able to get the benefits of being able to teach myself, but without the loss of social interaction (even parentally provided social interaction doesn't match up, in my opinion, as the people you're interacting with will likely be far less varied in nature).