Obviously almost every react native app out there is accessing a SQL db over the network, and they work fine. Are you seriously saying that it's slower to get data over the react native bridge than over the internet?
We are using a local database as a mirror for offline use, which is a key requirement. Profiling (a forgotten art nowadays) shows that most time spent during queries is in this bridge and not in the actual queries.
I know realm has a React Native library which I imagine you could use to access the db directly. Can you do something like that with SQLite? I.e access it without going through java/the bridge?