There’s no reliable way for bots to send whispers.
It doesn’t matter if its a normal account or a known/verified bot, it will still run into issues frequently.
Sending a whisper to a user who has whispered you first may help, or it may not. Twitch doesn’t disclose the specifics of its anti-spam measures so a lot of the information is just observations from people over the years.
tl;dr it’s not worth your time trying to get a bot to use whispers.