You can also validate this assertion with the App Privacy Report. Settings -> Privacy (& Security, if on iOS 16) -> App Privacy Report -> App Network Activity -> Show All -> all network activity will be here. Bouncer shouldn't be listed (or at least, it isn't on my device) because it doesn't use the network for this.
> Bouncer does not share, upload or send any of your personal information or SMS messages to a remote server. All the filtering happens locally on your phone, based on your own private word or regular expression list.