Places where you can copy the message content of a bot:
My Bots / [BotName] / View / Edit:
A tap & hold lets you select and copy any portion of the message content of the bot.
My Bots / [BotName] / Talk):
On the Talk Page, tap an individual message.
If the message has a pencil icon in the upper right corner, tap & hold lets you select and copy.
If it does not, a double-tap copies the whole message.
My Bots / [BotName] / Share / Share bot messages:
Here you can send a complete copy of the bot messages content to yourself.