We've heard from several in our chatbot community that their IDX providers said their website bounces have increased since the chatbot was installed. Actually, this statistic can be misleading.
The chatbot dialog runs under a separate URL than the parent website. When a visitor comes to your website, analytics records a visit. If that visitor starts to engage with the chatbot, they effectively 'leave' the parent website during the time they are conversing with the chatbot. Though this can look like the visitor 'bounced' from the website to another unrelated website, they actually are still viewing your IDX site and have full access at any time.
The most important thing we are looking for is engagement. We want site visitors to become bonafide leads. In our experience, once a visitor engages with the chatbot, they are more apt to provide contact information than if they had encountered a site without either human or chat interaction.