My daughter has been in Center daycare since she was 4 mo's, and just so you know...hindsight is always 20/20. Every parent questions every decision they make, as I have often questioned having her in a Center vs. Home, or even my staying home...so try not to be too hard on yourself.
Just so you know,...even though my child has been in daycare since an infant(now 4+), doesn't mean that she is NOT going to be picked on or vise-versa. We teach her values to be nice to everyone and never to hit teaching about why we treat people the way we do. Bullying will ALWAYS be an issue and keeping your child from daycare for 4 years did not teach your child to be bullied and not stand up for herself. There is a fine line in teaching about bullying vs. self defense. Some children are just more of the bullying type and I honestly believe that even at young ages, ALL children experience bullying either by doing it or being a victim of it. I sort of hope that all kids sort of take their turns being picked on at young ages so they ALL can feel how terribile it is to be picked on and singled out. Then, us parents and teachers can use their feelings as a way to relate to others when they themselves are the bullies. If it happens at young ages, hopefully they'll learn the lessons they need to cope when they get into jr.high and highschool where bullying is REALLY bad.
So, talk about the bullying issue with her and how we should never treat people meanly...and if you see someone being mean to someone else, or to you, stick up for them and help so that they don't feel hurt or sad.
I once picked up my daughter only to find her hair in someone elses hands while she just sat there and played with a toy upside down because the boy had her hair wound so tight around his hands that she couldn't move. She wasn't crying, but it was a perfect opportunity to teach her the lesson about standing up for herself.
Then, not too long after, when picking up my daughter, I saw her help a younger boy in the room after a bulling child started picking on him...she pushed the bully down on his butt for picking on her younger friend who didn't defend herself and was crying. Not that I condone that behavior, deep down in my heart, I was proud of her for sticking up to that bully and protecting her friend...even if it got her in trouble with the teacher, I believe she made the right decision.
So, use those experiences as lessons. I believe it's the only true way for children to relate to how others feel. And, again...don't be too hard on yourself for NOT putting her in daycare.
Building relationships and social skills never come too late and she'll catch on quickly no matter what the issue's are. She'll learn, children are spunges. You never know...perhaps keeping your child at home made her a nicer person in the long run for not being corrupted by the bad behaviors of others. It's truely amazing what kids pick up from other kids...and many are not good.