Many states in the United States allow a “belief exemption” for measles, mumps, and rubella (MMR) vaccines. People’s opinion on whether or not to take the vaccine can have direct consequences in public health. Social media has been one of the dominant communication channels for people to express their opinions of vaccination. Despite governmental organizations’ efforts of disseminating information of vaccination benefits, anti-vaccine sentiment is still gaining momentum. Studies have shown that bots on social media (i.e., social bots) can influence opinion trends by posting a substantial number of automated messages. The research presented here investigates the communication patterns of anti- and pro-vaccine users and the role of bots in Twitter by studying a retweet network related to MMR vaccine after the 2015 California Disneyland measles outbreak. We first classified the users into anti-vaccination, neutral to vaccination, and pro-vaccination groups using supervised machine learning. We discovered that pro- and anti-vaccine users retweet predominantly from their own opinion group. In addition, our bot analysis discovers that 1.45% of the corpus users were identified as likely bots which produced 4.59% of all tweets within our dataset. We further found that bots display hyper-social tendencies by initiating retweets at higher frequencies with users within the same opinion group. The article concludes that highly clustered anti-vaccine Twitter users make it difficult for health organizations to penetrate and counter opinionated information while social bots may be deepening this trend. We believe that these findings can be useful in developing strategies for health communication of vaccination.