No, Bob is not a gender-neutral name. It is overwhelmingly a male name.
"Bobby" is slightly closer to neutral, as it can be a shortened form of (among other possibilities) "Robert" (male) or "Roberta" (female). In the modern generation though this is still much more commonly a male name.
Gender-API.com, with which I am in no way affiliated, provides a gender inference service based on source data they describe as follows:
To provide the highest possible accuracy, we combine the data of multiple data sources. We use data from publicly available governmental sources and combine them with data we crawl from social networks, which provides you the best possible matches. Each name has to be verified by different sources to be added to our list.
The results for the name "Bob" are:
- Gender: male
- Accuracy: 99%
- Samples: 12966
I can't vouch for the scientific quality of their data, but I do empirically agree completely with the result. To my knowledge I have never met a "Bob" or "Bobby" who identified female (but I have met both male and female "Bobbie").